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Merge branch 'multi-objective' into future 

Former-commit-id: 2be06f51ca [formerly 44b6855fea]
Former-commit-id: cf79ec79b6
tempestpy_adaptions
TimQu 8 years ago
parent
ac4ef1d31e 48b82e7b14
commit
e06bef0996
228 changed files with 15744 additions and 795 deletions
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  1. 2
      CMakeLists.txt
  2. 18
      examples/fractions.sh
  3. 51
      examples/list.sh
  4. 61
      examples/list2.sh
  5. 54
      examples/listBenchmarks.sh
  6. 23
      examples/multiobjective/display_exported_plot.tex
  7. 93
      examples/multiobjective/ma/mutex/mutex2.ma
  8. 98
      examples/multiobjective/ma/mutex/mutex3.ma
  9. 103
      examples/multiobjective/ma/mutex/mutex4.ma
  10. 110
      examples/multiobjective/ma/mutex/mutex5.ma
  11. 101
      examples/multiobjective/ma/polling/polling.ma
  12. 1
      examples/multiobjective/ma/server/server.csl
  13. 34
      examples/multiobjective/ma/server/server.ma
  14. 1
      examples/multiobjective/ma/simple/simple.csl
  15. 15
      examples/multiobjective/ma/simple/simple.ma
  16. 45
      examples/multiobjective/ma/stream/stream.ma
  17. 1
      examples/multiobjective/ma/stream/stream_bounded_pareto.csl
  18. 2
      examples/multiobjective/ma/stream/stream_mixed_pareto.csl
  19. 1
      examples/multiobjective/ma/stream/stream_unbounded_pareto.csl
  20. 88
      examples/multiobjective/mdp/consensus/consensus2_3_2.nm
  21. 1
      examples/multiobjective/mdp/consensus/consensus2_3_2_numerical.pctl
  22. 1
      examples/multiobjective/mdp/consensus/consensus2_3_2_pareto.pctl
  23. 114
      examples/multiobjective/mdp/consensus/consensus2_4_2.nm
  24. 1
      examples/multiobjective/mdp/consensus/consensus2_4_2_numerical.pctl
  25. 1
      examples/multiobjective/mdp/consensus/consensus2_4_2_pareto.pctl
  26. 140
      examples/multiobjective/mdp/consensus/consensus2_5_2.nm
  27. 1
      examples/multiobjective/mdp/consensus/consensus2_5_2_numerical.pctl
  28. 1
      examples/multiobjective/mdp/consensus/consensus2_5_2_pareto.pctl
  29. 100
      examples/multiobjective/mdp/consensus/consensus3_3_2.nm
  30. 1
      examples/multiobjective/mdp/consensus/consensus3_3_2_numerical.pctl
  31. 1
      examples/multiobjective/mdp/consensus/consensus3_3_2_pareto.pctl
  32. 131
      examples/multiobjective/mdp/consensus/consensus3_4_2.nm
  33. 1
      examples/multiobjective/mdp/consensus/consensus3_4_2_numerical.pctl
  34. 1
      examples/multiobjective/mdp/consensus/consensus3_4_2_pareto.pctl
  35. 162
      examples/multiobjective/mdp/consensus/consensus3_5_2.nm
  36. 1
      examples/multiobjective/mdp/consensus/consensus3_5_2_numerical.pctl
  37. 1
      examples/multiobjective/mdp/consensus/consensus3_5_2_pareto.pctl
  38. 87
      examples/multiobjective/mdp/consensus/origFiles/consensus2_multi3.nm
  39. 113
      examples/multiobjective/mdp/consensus/origFiles/consensus2_multi4.nm
  40. 139
      examples/multiobjective/mdp/consensus/origFiles/consensus2_multi5.nm
  41. 99
      examples/multiobjective/mdp/consensus/origFiles/consensus3_multi3.nm
  42. 130
      examples/multiobjective/mdp/consensus/origFiles/consensus3_multi4.nm
  43. 161
      examples/multiobjective/mdp/consensus/origFiles/consensus3_multi5.nm
  44. 27
      examples/multiobjective/mdp/consensus/origFiles/consensus_multi.pctl
  45. 160
      examples/multiobjective/mdp/dpm/dpm100.nm
  46. 3
      examples/multiobjective/mdp/dpm/dpm100_numerical.pctl
  47. 1
      examples/multiobjective/mdp/dpm/dpm100_pareto.pctl
  48. 160
      examples/multiobjective/mdp/dpm/dpm200.nm
  49. 3
      examples/multiobjective/mdp/dpm/dpm200_numerical.pctl
  50. 1
      examples/multiobjective/mdp/dpm/dpm200_pareto.pctl
  51. 160
      examples/multiobjective/mdp/dpm/dpm300.nm
  52. 3
      examples/multiobjective/mdp/dpm/dpm300_numerical.pctl
  53. 1
      examples/multiobjective/mdp/dpm/dpm300_pareto.pctl
  54. 160
      examples/multiobjective/mdp/dpm/origFiles/power-timed.nm
  55. 11
      examples/multiobjective/mdp/dpm/origFiles/power-timed.pctl
  56. 8
      examples/multiobjective/mdp/scheduler/origFiles/scheduler.pctl
  57. 95
      examples/multiobjective/mdp/scheduler/origFiles/scheduler_prob2_K.nm
  58. 95
      examples/multiobjective/mdp/scheduler/scheduler05.nm
  59. 4
      examples/multiobjective/mdp/scheduler/scheduler05_numerical.pctl
  60. 4
      examples/multiobjective/mdp/scheduler/scheduler05_pareto.pctl
  61. 95
      examples/multiobjective/mdp/scheduler/scheduler25.nm
  62. 4
      examples/multiobjective/mdp/scheduler/scheduler25_numerical.pctl
  63. 4
      examples/multiobjective/mdp/scheduler/scheduler25_pareto.pctl
  64. 95
      examples/multiobjective/mdp/scheduler/scheduler50.nm
  65. 4
      examples/multiobjective/mdp/scheduler/scheduler50_numerical.pctl
  66. 4
      examples/multiobjective/mdp/scheduler/scheduler50_pareto.pctl
  67. 25
      examples/multiobjective/mdp/simple/simple.nm
  68. 2
      examples/multiobjective/mdp/simple/simple.pctl
  69. 231
      examples/multiobjective/mdp/team/origFiles/MDP_a2_r3_t2_full_exp.nm
  70. 287
      examples/multiobjective/mdp/team/origFiles/MDP_a3_r3_t2_full_exp.nm
  71. 364
      examples/multiobjective/mdp/team/origFiles/MDP_a4_r3_t2_full_exp.nm
  72. 531
      examples/multiobjective/mdp/team/origFiles/MDP_a5_r3_t2_full_exp.nm
  73. 45
      examples/multiobjective/mdp/team/origFiles/team.pctl
  74. 286
      examples/multiobjective/mdp/team/team2obj_3.nm
  75. 1
      examples/multiobjective/mdp/team/team2obj_3_numerical.pctl
  76. 1
      examples/multiobjective/mdp/team/team2obj_3_pareto.pctl
  77. 368
      examples/multiobjective/mdp/team/team2obj_4.nm
  78. 1
      examples/multiobjective/mdp/team/team2obj_4_numerical.pctl
  79. 1
      examples/multiobjective/mdp/team/team2obj_4_pareto.pctl
  80. 532
      examples/multiobjective/mdp/team/team2obj_5.nm
  81. 1
      examples/multiobjective/mdp/team/team2obj_5_numerical.pctl
  82. 1
      examples/multiobjective/mdp/team/team2obj_5_pareto.pctl
  83. 288
      examples/multiobjective/mdp/team/team3obj_3.nm
  84. 1
      examples/multiobjective/mdp/team/team3obj_3_numerical.pctl
  85. 1
      examples/multiobjective/mdp/team/team3obj_3_pareto.pctl
  86. 366
      examples/multiobjective/mdp/team/team3obj_4.nm
  87. 1
      examples/multiobjective/mdp/team/team3obj_4_numerical.pctl
  88. 1
      examples/multiobjective/mdp/team/team3obj_4_pareto.pctl
  89. 532
      examples/multiobjective/mdp/team/team3obj_5.nm
  90. 1
      examples/multiobjective/mdp/team/team3obj_5_numerical.pctl
  91. 1
      examples/multiobjective/mdp/team/team3obj_5_pareto.pctl
  92. 169
      examples/multiobjective/mdp/zeroconf-tb/origFiles/zeroconf_host_multi2_time.nm
  93. 174
      examples/multiobjective/mdp/zeroconf-tb/origFiles/zeroconf_host_multi4_time.nm
  94. 13
      examples/multiobjective/mdp/zeroconf-tb/origFiles/zeroconf_host_multi_time.pctl
  95. 169
      examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb2_14.nm
  96. 1
      examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb2_14_numerical.pctl
  97. 1
      examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb2_14_pareto.pctl
  98. 174
      examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb4_10.nm
  99. 1
      examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb4_10_numerical.pctl
  100. 1
      examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb4_10_pareto.pctl

2
CMakeLists.txt
View File

@ -30,6 +30,8 @@ option(STORM_USE_COTIRE "Sets whether Cotire should be used (for building precom
option(LINK_LIBCXXABI "Sets whether libc++abi should be linked." OFF)
option(USE_LIBCXX "Sets whether the standard library is libc++." OFF)
option(USE_CARL "Sets whether carl should be included." ON)
option(USE_SMTRAT "Sets whether SMT-RAT should be included." OFF)
option(USE_HYPRO "Sets whether HyPro should be included." OFF)
option(XML_SUPPORT "Sets whether xml based format parsing should be included." ON)
option(FORCE_COLOR "Force color output" OFF)
mark_as_advanced(FORCE_COLOR)

18
examples/fractions.sh
View File

@ -1,18 +0,0 @@
#!/bin/bash
executable="timeout 3600 ../build/src/storm"
arguments=" -i 1000000 --parametric --parametricRegion"
mkdir fractions
# pdtmcs
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=15,TotalRuns=5 --prop ./pdtmc/crowds/crowds.prctl --region:regionfile ./pdtmc/crowds/crowds_regions.txt $arguments | tee ./fractions/pdtmc_crowds.pm-constCrowdSize_15_TotalRuns_5.log
$executable -s ./pdtmc/nand/nand.pm -const N=10,K=5 --prop ./pdtmc/nand/nand.prctl --region:regionfile ./pdtmc/nand/nand_regions.txt $arguments | tee ./fractions/pdtmc_nand.pm-constN_10_K_5.log
$executable -s ./pdtmc/brp_rewards2/brp_rewards2.pm -const N=256,MAX=5 --prop ./pdtmc/brp_rewards2/brp_rewards2.prctl --region:regionfile ./pdtmc/brp_rewards2/brp_rewards2_regions.txt $arguments | tee ./fractions/pdtmc_brp_rewards2.pm-constN_256_MAX_5.log
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=256,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regionfile ./pdtmc/brp_rewards4/brp_rewards4_regions.txt $arguments | tee ./fractions/pdtmc_brp_rewards4.pm-constN_256_MAX_5.log
# pmdps
$executable -s ./pmdp/brp/brp.pm -const N=256,MAX=5 --prop ./pmdp/brp/brp.prctl --region:regionfile ./pmdp/brp/brp_regions.txt $arguments | tee ./fractions/pmdp_brp.pm-constN_256_MAX_5.log
$executable -s ./pmdp/coin4/coin4.pm -const K=2 --prop ./pmdp/coin4/coin4.prctl --region:regionfile ./pmdp/coin4/coin4_regions.txt $arguments | tee ./fractions/pmdp_coin4.pm-constK_4.log
$executable -s ./pmdp/zeroconf/zeroconf.pm -const K=2 --prop ./pmdp/zeroconf/zeroconf.prctl --region:regionfile ./pmdp/zeroconf/zeroconf_regions.txt $arguments | tee ./fractions/pmdp_zeroconf.pm-constK_5.log
$executable -s ./pmdp/reporter4/reporter4.pm -const Xsize=6,Ysize=6,MAXTRIES=2,B=2 --prop ./pmdp/reporter4/reporter4.prctl --region:regionfile ./pmdp/reporter4/reporter4_regions.txt $arguments | tee ./fractions/pmdp_reporter4.pm-constXsize_6_Ysize_6_MAXTRIES_2_B_2.log
wait
echo "done"

51
examples/list.sh
View File

@ -1,51 +0,0 @@
#!/bin/bash
executable="timeout 3600 ../build/src/storm"
arguments="-bisim -i 1000000 --parametric --parametricRegion --region:refinement 0.05 --region:samplemode off"
mkdir results
# pdtmcs
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=10,TotalRuns=5 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./results/pdtmc_crowds.pm-constCrowdSize_10_TotalRuns_5.log &
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=20,TotalRuns=10 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./results/pdtmc_crowds.pm-constCrowdSize_20_TotalRuns_10.log &
$executable -s ./pdtmc/nand/nand.pm -const N=10,K=5 --prop ./pdtmc/nand/nand.prctl --region:regions "0.000010<=perr<=0.999990,0.000010<=prob1<=0.999990;" $arguments | tee ./results/pdtmc_nand.pm-constN_10_K_5.log &
$executable -s ./pdtmc/nand/nand.pm -const N=25,K=5 --prop ./pdtmc/nand/nand.prctl --region:regions "0.000010<=perr<=0.999990,0.000010<=prob1<=0.999990;" $arguments | tee ./results/pdtmc_nand.pm-constN_25_K_5.log &
wait
$executable -s ./pdtmc/brp_rewards2/brp_rewards2.pm -const N=512,MAX=5 --prop ./pdtmc/brp_rewards2/brp_rewards2.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./results/pdtmc_brp_rewards2.pm-constN_512_MAX_5.log &
$executable -s ./pdtmc/brp_rewards2/brp_rewards2.pm -const N=4096,MAX=5 --prop ./pdtmc/brp_rewards2/brp_rewards2.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./results/pdtmc_brp_rewards2.pm-constN_4096_MAX_5.log &
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=256,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990,0.000010<=TOMsg<=0.999990,0.000010<=TOAck<=0.999990;" $arguments | tee ./results/pdtmc_brp_rewards4.pm-constN_256_MAX_5.log &
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=5012,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990,0.000010<=TOMsg<=0.999990,0.000010<=TOAck<=0.999990;" $arguments | tee ./results/pdtmc_brp_rewards4.pm-constN_5012_MAX_5.log &
$executable -s ./pdtmc/brp/brp.pm -const N=256,MAX=5 --prop ./pdtmc/brp/brp.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./results/pdtmc_brp.pm-constN_256_MAX_5.log &
$executable -s ./pdtmc/brp/brp.pm -const N=4096,MAX=5 --prop ./pdtmc/brp/brp.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./results/pdtmc_brp.pm-constN_4096_MAX_5.log &
wait
# pmdps
arguments="-i 1000000 --parametric --parametricRegion --region:refinement 0.05 --region:samplemode off"
$executable -s ./pmdp/brp/brp.pm -const N=256,MAX=5 --prop ./pmdp/brp/brp.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./results/pmdp_brp.pm-constN_256_MAX_5.log &
$executable -s ./pmdp/brp/brp.pm -const N=4096,MAX=5 --prop ./pmdp/brp/brp.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./results/pmdp_brp.pm-constN_4096_MAX_5.log &
$executable -s ./pmdp/coin2/coin2.pm -const K=2 --prop ./pmdp/coin2/coin2.prctl --region:regions "0.000010<=p1<=0.999990,0.000010<=p2<=0.999990;" $arguments | tee ./results/pmdp_coin2.pm-constK_2.log &
$executable -s ./pmdp/coin2/coin2.pm -const K=32 --prop ./pmdp/coin2/coin2.prctl --region:regions "0.000010<=p1<=0.999990,0.000010<=p2<=0.999990;" $arguments | tee ./results/pmdp_coin2.pm-constK_32.log &
$executable -s ./pmdp/coin4/coin4.pm -const K=2 --prop ./pmdp/coin4/coin4.prctl --region:regions "0.000010<=p1<=0.999990,0.000010<=p2<=0.999990,0.000010<=p3<=0.999990,0.000010<=p4<=0.999990;" $arguments | tee ./results/pmdp_coin4.pm-constK_2.log &
$executable -s ./pmdp/coin4/coin4.pm -const K=4 --prop ./pmdp/coin4/coin4.prctl --region:regions "0.000010<=p1<=0.999990,0.000010<=p2<=0.999990,0.000010<=p3<=0.999990,0.000010<=p4<=0.999990;" $arguments | tee ./results/pmdp_coin4.pm-constK_4.log &
wait
$executable -s ./pmdp/zeroconf/zeroconf.pm -const K=2 --prop ./pmdp/zeroconf/zeroconf.prctl --region:regions "0.000010<=loss<=0.999990,0.000010<=old<=0.999990;" $arguments | tee ./results/pmdp_zeroconf.pm-constK_2.log &
$executable -s ./pmdp/zeroconf/zeroconf.pm -const K=5 --prop ./pmdp/zeroconf/zeroconf.prctl --region:regions "0.000010<=loss<=0.999990,0.000010<=old<=0.999990;" $arguments | tee ./results/pmdp_zeroconf.pm-constK_5.log &
$executable -s ./pmdp/reporter2/reporter2.pm -const Xsize=6,Ysize=6,MAXTRIES=2,B=2 --prop ./pmdp/reporter2/reporter2.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pH<=0.999990;" $arguments | tee ./results/pmdp_reporter2.pm-constXsize_6_Ysize_6_MAXTRIES_2_B_2.log &
$executable -s ./pmdp/reporter2/reporter2.pm -const Xsize=100,Ysize=100,MAXTRIES=10,B=10 --prop ./pmdp/reporter2/reporter2.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pH<=0.999990;" $arguments | tee ./results/pmdp_reporter2.pm-constXsize_100_Ysize_100_MAXTRIES_10_B_10.log &
$executable -s ./pmdp/reporter4/reporter4.pm -const Xsize=6,Ysize=6,MAXTRIES=2,B=2 --prop ./pmdp/reporter4/reporter4.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pH<=0.999990,0.000010<=pLDiff<=0.999990,0.000010<=pHDiff<=0.999990;" $arguments | tee ./results/pmdp_reporter4.pm-constXsize_6_Ysize_6_MAXTRIES_2_B_2.log &
$executable -s ./pmdp/reporter4/reporter4.pm -const Xsize=10,Ysize=10,MAXTRIES=3,B=3 --prop ./pmdp/reporter4/reporter4.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pH<=0.999990,0.000010<=pLDiff<=0.999990,0.000010<=pHDiff<=0.999990;" $arguments | tee ./results/pmdp_reporter4.pm-constXsize_10_Ysize_10_MAXTRIES_3_B_3.log &
wait
echo "done!"

61
examples/list2.sh
View File

@ -1,61 +0,0 @@
#!/bin/bash
executable="timeout 3600 ../build/src/storm"
arguments="-i 1000000 --parametric --parametricRegion --region:refinement 0.05 --region:samplemode off"
resultfolder=res
mkdir $resultfolder
# pdtmcs
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=10,TotalRuns=5 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_10_TotalRuns_5.log &
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=15,TotalRuns=5 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_15_TotalRuns_5.log &
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=15,TotalRuns=7 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_15_TotalRuns_7.log &
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=20,TotalRuns=5 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_20_TotalRuns_5.log &
wait
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=20,TotalRuns=7 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_20_TotalRuns_7.log &
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=20,TotalRuns=10 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_20_TotalRuns_10.log &
$executable -s ./pdtmc/nand/nand.pm -const N=10,K=5 --prop ./pdtmc/nand/nand.prctl --region:regions "0.000010<=perr<=0.999990,0.000010<=prob1<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_nand.pm-constN_10_K_5.log &
$executable -s ./pdtmc/nand/nand.pm -const N=25,K=5 --prop ./pdtmc/nand/nand.prctl --region:regions "0.000010<=perr<=0.999990,0.000010<=prob1<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_nand.pm-constN_25_K_5.log &
wait
$executable -s ./pdtmc/brp_rewards2/brp_rewards2.pm -const N=256,MAX=5 --prop ./pdtmc/brp_rewards2/brp_rewards2.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards2.pm-constN_256_MAX_5.log &
$executable -s ./pdtmc/brp_rewards2/brp_rewards2.pm -const N=512,MAX=5 --prop ./pdtmc/brp_rewards2/brp_rewards2.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards2.pm-constN_512_MAX_5.log &
$executable -s ./pdtmc/brp_rewards2/brp_rewards2.pm -const N=4096,MAX=5 --prop ./pdtmc/brp_rewards2/brp_rewards2.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards2.pm-constN_4096_MAX_5.log &
wait
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=64,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990,0.000010<=TOMsg<=0.999990,0.000010<=TOAck<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards4.pm-constN_64_MAX_5.log &
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=128,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990,0.000010<=TOMsg<=0.999990,0.000010<=TOAck<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards4.pm-constN_128_MAX_5.log &
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=256,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regionso "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990,0.000010<=TOMsg<=0.999990,0.000010<=TOAck<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards4.pm-constN_256_MAX_5.log &
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=5012,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regionso "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990,0.000010<=TOMsg<=0.999990,0.000010<=TOAck<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards4.pm-constN_5012_MAX_5.log &
wait
$executable -s ./pdtmc/brp/brp.pm -const N=256,MAX=5 --prop ./pdtmc/brp/brp.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp.pm-constN_256_MAX_5.log &
$executable -s ./pdtmc/brp/brp.pm -const N=4096,MAX=5 --prop ./pdtmc/brp/brp.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp.pm-constN_4096_MAX_5.log &
wait
# New instances!!!!! (tested here also with bisim)
arguments="-bisim -i 1000000 --parametric --parametricRegion --region:refinement 0.05 --region:samplemode off"
resultfolder=res_bisim
mkdir $resultfolder
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=15,TotalRuns=5 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_15_TotalRuns_5.log &
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=15,TotalRuns=7 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_15_TotalRuns_7.log &
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=20,TotalRuns=5 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_20_TotalRuns_5.log &
wait
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=20,TotalRuns=7 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_20_TotalRuns_7.log &
$executable -s ./pdtmc/crowds/crowds.pm -const CrowdSize=20,TotalRuns=10 --prop ./pdtmc/crowds/crowds.prctl --region:regions "0.000010<=PF<=0.999990,0.000010<=badC<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_crowds.pm-constCrowdSize_20_TotalRuns_10.log &
wait
$executable -s ./pdtmc/brp_rewards2/brp_rewards2.pm -const N=256,MAX=5 --prop ./pdtmc/brp_rewards2/brp_rewards2.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards2.pm-constN_256_MAX_5.log &
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=64,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990,0.000010<=TOMsg<=0.999990,0.000010<=TOAck<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards4.pm-constN_64_MAX_5.log &
$executable -s ./pdtmc/brp_rewards4/brp_rewards4.pm -const N=128,MAX=5 --prop ./pdtmc/brp_rewards4/brp_rewards4.prctl --region:regions "0.000010<=pL<=0.999990,0.000010<=pK<=0.999990,0.000010<=TOMsg<=0.999990,0.000010<=TOAck<=0.999990;" $arguments | tee ./$resultfolder/pdtmc_brp_rewards4.pm-constN_128_MAX_5.log &
wait
echo "done!"

54
examples/listBenchmarks.sh
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@ -1,54 +0,0 @@
#!/bin/bash
if [ "$#" != 1 ];
then
echo "Wrong number of arguments! Provide a filename for the results!"
elif [ -a $1 ]; then
echo "File for results already exists!"
else
DIR="."
echo '#!/bin/bash' >> $1
echo 'executable="timeout 3600 ../build/src/storm"' >> $1
echo 'arguments="-bisim -i 1000000 --parametric --parametricRegion --region:refinement 0.05 --region:samplemode off"' >> $1
echo "mkdir results" >> $1
declare -a modeltypes=("pdtmc" "pmdp")
for modeltype in "${modeltypes[@]}"
do
if [ "$modeltype" == "pdtmc" ];
then
declare -a models=("crowds" "nand" "brp_rewards2" "brp_rewards4" "brp")
dobisim="-bisim"
else
declare -a models=("brp" "coin2" "coin4" "zeroconf" "reporter2" "reporter4")
dobisim=""
fi
echo "# $modeltype""s" >> $1
for model in "${models[@]}"
do
modelfolder="$DIR/$modeltype/$model"
suffix="-"
while read instance;
do
output='$executable '
output="$output""-s $modelfolder/$instance --prop $modelfolder/$model.prctl --region:regions "
region=$(head -n 1 $modelfolder/$model"_space.txt")
region="$(echo -e "${region}" | tr -d '[[:space:]]')"
output="$output"'"'$region'" $arguments | tee '
instanceString="$(echo -e "${instance}" | tr -d '[[:space:]]')"
instanceString=${instanceString//[,=]/_}
output="$output""./results/$modeltype""_$instanceString.log &"
echo $output >> $1
done < "$modelfolder/models"
done
done
echo 'wait' >> $1
fi

23
examples/multiobjective/display_exported_plot.tex
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% This file can be used to display the exported plots from multi-objective model checking
\documentclass{article}
\usepackage{pgfplots}
\usepackage{filecontents}
\newcommand{\resultPath}{../ma/stream/results/}
\begin{document}
\centering
\begin{tikzpicture}[scale=1.75]
\begin{axis}[
enlargelimits=false,
axis background/.style={fill=red!50}
]
\addplot[fill=white, very thin] table [col sep=comma] {\resultPath overapproximation.csv} -- cycle;
\addplot[fill=green, very thin] table [col sep=comma] {\resultPath underapproximation.csv} -- cycle;
\addplot[mark=o, mark options={blue, scale=1.3, thick}, only marks] table [col sep=comma] {\resultPath paretopoints.csv};
\addplot[mark=false] table [col sep=comma] {\resultPath boundaries.csv};
\end{axis}
\end{tikzpicture}
\end{document}

93
examples/multiobjective/ma/mutex/mutex2.ma
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// Translation of the MAPA Specification of a mutex system into PRISM code
// http://wwwhome.cs.utwente.nl/~timmer/scoop/papers/qest13/index.html
ma
const int N; // The size of the data (should be at most 6)
formula someEnter = s1=1 | s2=1;
formula someWait = s1=2 | s2=2;
formula someLow = s1=3 | s2=3;
formula someHigh = s1=4 | s2=4;
formula someTie = s1=5 | s2=5;
formula someAdmit = s1=6 | s2=6;
formula otherHigh = s2=4;
formula someLowTie = someLow | someTie;
formula someLowHighTie = someLow | someHigh | someTie;
formula someAdmitHighTie = someAdmit | someHigh | someTie;
formula someEnterWait = someEnter | someWait;
module process1
// The internal state of the process
// 0: uninterested
// 1: enter
// 2: wait
// 3: low
// 4: high
// 5: tie
// 6: admit
s1 : [0..6];
// the phase of the protocol
phase1 : [1..12];
// The considered data
data1 : [1..N];
// The result of a coin flip
h1 : bool;
//[] phase1=1 -> 1 : true;
[] phase1=1 -> 1 : (phase1'=2);
[] phase1=2 & N>=1 -> 1 : (data1'=1) & (phase1'=3);
[] phase1=2 & N>=2 -> 1 : (data1'=2) & (phase1'=3);
[] phase1=2 & N>=3 -> 1 : (data1'=3) & (phase1'=3);
[] phase1=2 & N>=4 -> 1 : (data1'=4) & (phase1'=3);
[] phase1=2 & N>=5 -> 1 : (data1'=5) & (phase1'=3);
[] phase1=2 & N>=6 -> 1 : (data1'=6) & (phase1'=3);
[] phase1=3 & (someLowHighTie & !someAdmit) -> 1 : (s1'=2) & (phase1'=4);
[] phase1=3 & (!someLowHighTie | someAdmit) -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
[] phase1=4 & (!someLowHighTie | someAdmit) -> 1 : (s1'=1) & (phase1'=3);
[] phase1=5 & h1=false -> 1 : (s1'=3) & (phase1'=6);
[] phase1=5 & h1=true -> 1 : (s1'=4) & (phase1'=7) & (h1'=false);
[] phase1=6 & !someAdmitHighTie -> 1 : (s1'=5) & (phase1'=8);
[] phase1=7 & (someAdmit | otherHigh) -> 1 : (s1'=5) & (phase1'=9);
[] phase1=7 & (!someAdmit & !otherHigh) -> 1 : (phase1'=10);
[] phase1=8 -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
[] phase1=9 & !someAdmit & !otherHigh -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
<> phase1=10 -> data1 : (phase1'=11) & (data1'=1);
[] phase1=11 & (someLowTie | otherHigh) & !someEnter -> 1 : (s1'=0) & (phase1'=1);
[] phase1=11 & !someLowTie & !otherHigh -> 1 : (s1'=6) & (phase1'=12);
[] phase1=12 & !someEnterWait -> 1 : (s1'=0) & (phase1'=1);
endmodule
module process2 = process1 [ s1=s2, phase1=phase2, data1=data2, h1=h2, s2=s1] endmodule
label "crit1" = phase1=10;
label "crit2" = phase2=10;
rewards "timeInCrit1"
phase1=10 : 1;
endrewards
rewards "timeInCrit2"
phase2=10 : 1;
endrewards

98
examples/multiobjective/ma/mutex/mutex3.ma
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// Translation of the MAPA Specification of a mutex system into PRISM code
// http://wwwhome.cs.utwente.nl/~timmer/scoop/papers/qest13/index.html
ma
const int N; // The size of the data (should be at most 6)
formula someEnter = s1=1 | s2=1 | s3=1;
formula someWait = s1=2 | s2=2 | s3=2;
formula someLow = s1=3 | s2=3 | s3=3;
formula someHigh = s1=4 | s2=4 | s3=4;
formula someTie = s1=5 | s2=5 | s3=5;
formula someAdmit = s1=6 | s2=6 | s3=6;
formula otherHigh = s2=4 | s3=4;
formula someLowTie = someLow | someTie;
formula someLowHighTie = someLow | someHigh | someTie;
formula someAdmitHighTie = someAdmit | someHigh | someTie;
formula someEnterWait = someEnter | someWait;
module process1
// The internal state of the process
// 0: uninterested
// 1: enter
// 2: wait
// 3: low
// 4: high
// 5: tie
// 6: admit
s1 : [0..6];
// the phase of the protocol
phase1 : [1..12];
// The considered data
data1 : [1..N];
// The result of a coin flip
h1 : bool;
//[] phase1=1 -> 1 : true;
[] phase1=1 -> 1 : (phase1'=2);
[] phase1=2 & N>=1 -> 1 : (data1'=1) & (phase1'=3);
[] phase1=2 & N>=2 -> 1 : (data1'=2) & (phase1'=3);
[] phase1=2 & N>=3 -> 1 : (data1'=3) & (phase1'=3);
[] phase1=2 & N>=4 -> 1 : (data1'=4) & (phase1'=3);
[] phase1=2 & N>=5 -> 1 : (data1'=5) & (phase1'=3);
[] phase1=2 & N>=6 -> 1 : (data1'=6) & (phase1'=3);
[] phase1=3 & (someLowHighTie & !someAdmit) -> 1 : (s1'=2) & (phase1'=4);
[] phase1=3 & (!someLowHighTie | someAdmit) -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
[] phase1=4 & (!someLowHighTie | someAdmit) -> 1 : (s1'=1) & (phase1'=3);
[] phase1=5 & h1=false -> 1 : (s1'=3) & (phase1'=6);
[] phase1=5 & h1=true -> 1 : (s1'=4) & (phase1'=7) & (h1'=false);
[] phase1=6 & !someAdmitHighTie -> 1 : (s1'=5) & (phase1'=8);
[] phase1=7 & (someAdmit | otherHigh) -> 1 : (s1'=5) & (phase1'=9);
[] phase1=7 & (!someAdmit & !otherHigh) -> 1 : (phase1'=10);
[] phase1=8 -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
[] phase1=9 & !someAdmit & !otherHigh -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
<> phase1=10 -> data1 : (phase1'=11) & (data1'=1);
[] phase1=11 & (someLowTie | otherHigh) & !someEnter -> 1 : (s1'=0) & (phase1'=1);
[] phase1=11 & !someLowTie & !otherHigh -> 1 : (s1'=6) & (phase1'=12);
[] phase1=12 & !someEnterWait -> 1 : (s1'=0) & (phase1'=1);
endmodule
module process2 = process1 [ s1=s2, phase1=phase2, data1=data2, h1=h2, s2=s1] endmodule
module process3 = process1 [ s1=s3, phase1=phase3, data1=data3, h1=h3, s3=s1] endmodule
label "crit1" = phase1=10;
label "crit2" = phase2=10;
label "crit3" = phase3=10;
rewards "timeInCrit1"
phase1=10 : 1;
endrewards
rewards "timeInCrit2"
phase2=10 : 1;
endrewards
rewards "timeInCrit3"
phase3=10 : 1;
endrewards

103
examples/multiobjective/ma/mutex/mutex4.ma
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// Translation of the MAPA Specification of a mutex system into PRISM code
// http://wwwhome.cs.utwente.nl/~timmer/scoop/papers/qest13/index.html
ma
const int N; // The size of the data (should be at most 6)
formula someEnter = s1=1 | s2=1 | s3=1 | s4=1;
formula someWait = s1=2 | s2=2 | s3=2 | s4=2;
formula someLow = s1=3 | s2=3 | s3=3 | s4=3;
formula someHigh = s1=4 | s2=4 | s3=4 | s4=4;
formula someTie = s1=5 | s2=5 | s3=5 | s4=5;
formula someAdmit = s1=6 | s2=6 | s3=6 | s4=6;
formula otherHigh = s2=4 | s3=4 | s4=4;
formula someLowTie = someLow | someTie;
formula someLowHighTie = someLow | someHigh | someTie;
formula someAdmitHighTie = someAdmit | someHigh | someTie;
formula someEnterWait = someEnter | someWait;
module process1
// The internal state of the process
// 0: uninterested
// 1: enter
// 2: wait
// 3: low
// 4: high
// 5: tie
// 6: admit
s1 : [0..6];
// the phase of the protocol
phase1 : [1..12];
// The considered data
data1 : [1..N];
// The result of a coin flip
h1 : bool;
//[] phase1=1 -> 1 : true;
[] phase1=1 -> 1 : (phase1'=2);
[] phase1=2 & N>=1 -> 1 : (data1'=1) & (phase1'=3);
[] phase1=2 & N>=2 -> 1 : (data1'=2) & (phase1'=3);
[] phase1=2 & N>=3 -> 1 : (data1'=3) & (phase1'=3);
[] phase1=2 & N>=4 -> 1 : (data1'=4) & (phase1'=3);
[] phase1=2 & N>=5 -> 1 : (data1'=5) & (phase1'=3);
[] phase1=2 & N>=6 -> 1 : (data1'=6) & (phase1'=3);
[] phase1=3 & (someLowHighTie & !someAdmit) -> 1 : (s1'=2) & (phase1'=4);
[] phase1=3 & (!someLowHighTie | someAdmit) -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
[] phase1=4 & (!someLowHighTie | someAdmit) -> 1 : (s1'=1) & (phase1'=3);
[] phase1=5 & h1=false -> 1 : (s1'=3) & (phase1'=6);
[] phase1=5 & h1=true -> 1 : (s1'=4) & (phase1'=7) & (h1'=false);
[] phase1=6 & !someAdmitHighTie -> 1 : (s1'=5) & (phase1'=8);
[] phase1=7 & (someAdmit | otherHigh) -> 1 : (s1'=5) & (phase1'=9);
[] phase1=7 & (!someAdmit & !otherHigh) -> 1 : (phase1'=10);
[] phase1=8 -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
[] phase1=9 & !someAdmit & !otherHigh -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
<> phase1=10 -> data1 : (phase1'=11) & (data1'=1);
[] phase1=11 & (someLowTie | otherHigh) & !someEnter -> 1 : (s1'=0) & (phase1'=1);
[] phase1=11 & !someLowTie & !otherHigh -> 1 : (s1'=6) & (phase1'=12);
[] phase1=12 & !someEnterWait -> 1 : (s1'=0) & (phase1'=1);
endmodule
module process2 = process1 [ s1=s2, phase1=phase2, data1=data2, h1=h2, s2=s1] endmodule
module process3 = process1 [ s1=s3, phase1=phase3, data1=data3, h1=h3, s3=s1] endmodule
module process4 = process1 [ s1=s4, phase1=phase4, data1=data4, h1=h4, s4=s1] endmodule
label "crit1" = phase1=10;
label "crit2" = phase2=10;
label "crit3" = phase3=10;
label "crit4" = phase4=10;
rewards "timeInCrit1"
phase1=10 : 1;
endrewards
rewards "timeInCrit2"
phase2=10 : 1;
endrewards
rewards "timeInCrit3"
phase3=10 : 1;
endrewards
rewards "timeInCrit4"
phase4=10 : 1;
endrewards

110
examples/multiobjective/ma/mutex/mutex5.ma
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// Translation of the MAPA Specification of a mutex system into PRISM code
// http://wwwhome.cs.utwente.nl/~timmer/scoop/papers/qest13/index.html
ma
const int N; // The size of the data (should be at most 6)
formula someEnter = s1=1 | s2=1 | s3=1 | s4=1 | s5=1;
formula someWait = s1=2 | s2=2 | s3=2 | s4=2 | s5=2;
formula someLow = s1=3 | s2=3 | s3=3 | s4=3 | s5=3;
formula someHigh = s1=4 | s2=4 | s3=4 | s4=4 | s5=4;
formula someTie = s1=5 | s2=5 | s3=5 | s4=5 | s5=5;
formula someAdmit = s1=6 | s2=6 | s3=6 | s4=6 | s5=6;
formula otherHigh = s2=4 | s3=4 | s4=4 | s5=4;
formula someLowTie = someLow | someTie;
formula someLowHighTie = someLow | someHigh | someTie;
formula someAdmitHighTie = someAdmit | someHigh | someTie;
formula someEnterWait = someEnter | someWait;
module process1
// The internal state of the process
// 0: uninterested
// 1: enter
// 2: wait
// 3: low
// 4: high
// 5: tie
// 6: admit
s1 : [0..6];
// the phase of the protocol
phase1 : [1..12];
// The considered data
data1 : [1..N];
// The result of a coin flip
h1 : bool;
//[] phase1=1 -> 1 : true;
[] phase1=1 -> 1 : (phase1'=2);
[] phase1=2 & N>=1 -> 1 : (data1'=1) & (phase1'=3);
[] phase1=2 & N>=2 -> 1 : (data1'=2) & (phase1'=3);
[] phase1=2 & N>=3 -> 1 : (data1'=3) & (phase1'=3);
[] phase1=2 & N>=4 -> 1 : (data1'=4) & (phase1'=3);
[] phase1=2 & N>=5 -> 1 : (data1'=5) & (phase1'=3);
[] phase1=2 & N>=6 -> 1 : (data1'=6) & (phase1'=3);
[] phase1=3 & (someLowHighTie & !someAdmit) -> 1 : (s1'=2) & (phase1'=4);
[] phase1=3 & (!someLowHighTie | someAdmit) -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
[] phase1=4 & (!someLowHighTie | someAdmit) -> 1 : (s1'=1) & (phase1'=3);
[] phase1=5 & h1=false -> 1 : (s1'=3) & (phase1'=6);
[] phase1=5 & h1=true -> 1 : (s1'=4) & (phase1'=7) & (h1'=false);
[] phase1=6 & !someAdmitHighTie -> 1 : (s1'=5) & (phase1'=8);
[] phase1=7 & (someAdmit | otherHigh) -> 1 : (s1'=5) & (phase1'=9);
[] phase1=7 & (!someAdmit & !otherHigh) -> 1 : (phase1'=10);
[] phase1=8 -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
[] phase1=9 & !someAdmit & !otherHigh -> 0.5 : (phase1'=5) & (h1'=false) + 0.5 : (phase1'=5) & (h1'=true);
<> phase1=10 -> data1 : (phase1'=11) & (data1'=1);
[] phase1=11 & (someLowTie | otherHigh) & !someEnter -> 1 : (s1'=0) & (phase1'=1);
[] phase1=11 & !someLowTie & !otherHigh -> 1 : (s1'=6) & (phase1'=12);
[] phase1=12 & !someEnterWait -> 1 : (s1'=0) & (phase1'=1);
endmodule
module process2 = process1 [ s1=s2, phase1=phase2, data1=data2, h1=h2, s2=s1] endmodule
module process3 = process1 [ s1=s3, phase1=phase3, data1=data3, h1=h3, s3=s1] endmodule
module process4 = process1 [ s1=s4, phase1=phase4, data1=data4, h1=h4, s4=s1] endmodule
module process5 = process1 [ s1=s5, phase1=phase5, data1=data5, h1=h5, s5=s1] endmodule
label "crit1" = phase1=10;
label "crit2" = phase2=10;
label "crit3" = phase3=10;
label "crit4" = phase4=10;
label "crit5" = phase5=10;
rewards "timeInCrit1"
phase1=10 : 1;
endrewards
rewards "timeInCrit2"
phase2=10 : 1;
endrewards
rewards "timeInCrit3"
phase3=10 : 1;
endrewards
rewards "timeInCrit4"
phase4=10 : 1;
endrewards
rewards "timeInCrit5"
phase5=10 : 1;
endrewards

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examples/multiobjective/ma/polling/polling.ma
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// Translation of the MAPA Specification of a polling system into PRISM code
// http://wwwhome.cs.utwente.nl/~timmer/scoop/papers/qest13/index.html
ma
const int N; // number of job types (should be at most 6)
const int Q; // Maximum queue size in each station
// Formulae to control the LIFO queue of the stations.
// The queue is represented by some integer whose base N representation has at most Q digits, each representing one of the job types 0, 1, ..., N-1.
// In addition, we store the current size of the queue which is needed to distinguish an empty queue from a queue holding job of type 0
formula queue1_empty = q1Size=0;
formula queue1_full = q1Size=Q;
formula queue1_pop = floor(q1/N);
formula queue1_head = q1 - (queue1_pop * N); // i.e. q1 modulo N
formula queue1_push = q1*N;
formula queue2_empty = q2Size=0;
formula queue2_full = q2Size=Q;
formula queue2_pop = floor(q2/N);
formula queue2_head = q2 - (queue2_pop * N); // i.e. q2 modulo N
formula queue2_push = q2*N;
const int queue_maxValue = (N^Q)-1;
const double inRate1 = 3; // = (2 * #station) + 1;
const double inRate2 = 5; // = (2 * #station) + 1;
module pollingsys
// The queues for the stations
q1 : [0..queue_maxValue];
q1Size : [0..Q];
q2 : [0..queue_maxValue];
q2Size : [0..Q];
// Store the job that is currently processed by the server. j=N means that no job is processed.
j : [0..N] init N;
// Flag indicating whether a new job arrived
newJob1 : bool init false;
newJob2 : bool init false;
//<> !newJob1 & !newJob2 & !queue1_full & queue2_full & j=N -> inRate1 : (newJob1'=true);
//<> !newJob1 & !newJob2 & queue1_full & !queue2_full & j=N -> inRate2 : (newJob2'=true);
<> !newJob1 & !newJob2 & !queue1_full & !queue2_full & j=N -> inRate1 : (newJob1'=true) + inRate2 : (newJob2'=true);
<> !newJob1 & !newJob2 & queue1_full & queue2_full & j<N -> 2*(j+1) : (j'=N);
<> !newJob1 & !newJob2 & !queue1_full & queue2_full & j<N -> inRate1 : (newJob1'=true) + 2*(j+1) : (j'=N);
<> !newJob1 & !newJob2 & queue1_full & !queue2_full & j<N -> inRate2 : (newJob2'=true) + 2*(j+1) : (j'=N);
<> !newJob1 & !newJob2 & !queue1_full & !queue2_full & j<N -> inRate1 : (newJob1'=true) + inRate2 : (newJob2'=true) + 2*(j+1) : (j'=N);
[] newJob1 & N>=1 -> 1 : (q1Size'=q1Size+1) & (q1'=queue1_push+0) & (newJob1'=false);
[] newJob1 & N>=2 -> 1 : (q1Size'=q1Size+1) & (q1'=queue1_push+1) & (newJob1'=false);
[] newJob1 & N>=3 -> 1 : (q1Size'=q1Size+1) & (q1'=queue1_push+2) & (newJob1'=false);
[] newJob1 & N>=4 -> 1 : (q1Size'=q1Size+1) & (q1'=queue1_push+3) & (newJob1'=false);
[] newJob1 & N>=5 -> 1 : (q1Size'=q1Size+1) & (q1'=queue1_push+4) & (newJob1'=false);
[] newJob1 & N>=6 -> 1 : (q1Size'=q1Size+1) & (q1'=queue1_push+5) & (newJob1'=false);
[] newJob2 & N>=1 -> 1 : (q2Size'=q2Size+1) & (q2'=queue2_push+0) & (newJob2'=false);
[] newJob2 & N>=2 -> 1 : (q2Size'=q2Size+1) & (q2'=queue2_push+1) & (newJob2'=false);
[] newJob2 & N>=3 -> 1 : (q2Size'=q2Size+1) & (q2'=queue2_push+2) & (newJob2'=false);
[] newJob2 & N>=4 -> 1 : (q2Size'=q2Size+1) & (q2'=queue2_push+3) & (newJob2'=false);
[] newJob2 & N>=5 -> 1 : (q2Size'=q2Size+1) & (q2'=queue2_push+4) & (newJob2'=false);
[] newJob2 & N>=6 -> 1 : (q2Size'=q2Size+1) & (q2'=queue2_push+5) & (newJob2'=false);
[copy1] !newJob1 & !newJob2 & !queue1_empty & j=N -> 0.9 : (j'=queue1_head) & (q1Size'=q1Size-1) & (q1'=queue1_pop) + 0.1 : (j'=queue1_head);
[copy2] !newJob1 & !newJob2 & !queue2_empty & j=N -> 0.9 : (j'=queue2_head) & (q2Size'=q2Size-1) & (q2'=queue2_pop) + 0.1 : (j'=queue2_head);
endmodule
label "q1full" = q1Size=Q;
label "q2full" = q2Size=Q;
label "allqueuesfull" = q1Size=Q & q2Size=Q;
// Rewards adapted from Guck et al.: Modelling and Analysis of Markov Reward Automata
rewards "processedjobs1"
[copy1] true : 0.1;
endrewards
rewards "processedjobs2"
[copy1] true : 0.1;
endrewards
rewards "processedjobs"
[copy1] true : 1;
[copy2] true : 1;
endrewards
rewards "waiting1"
true : (q1Size);
endrewards
rewards "waiting2"
true : (q2Size);
endrewards
rewards "waiting"
true : (q1Size + q2Size);
endrewards

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examples/multiobjective/ma/server/server.csl
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multi(Tmax=? [ F "error" ], Pmax=? [ F "processB" ])

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examples/multiobjective/ma/server/server.ma
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ma
const double rateProcessing = 2;
const double rateA = 1;
const double rateB = 1;
module server
s : [0..5]; // current state:
// 0: wait for request
// 1: received request from A
// 2: received request from B
// 3: starting to process request of B
// 4: processing request
// 5: error
<> s=0 -> rateA : (s'=1) + rateB : (s'=2);
[alpha] s=1 -> 1 : (s'=4);
[alpha] s=2 -> 1 : (s'=3);
[beta] s=2 -> 0.5 : (s'=0) + 0.5 : (s'=3);
[] s=3 -> 1 : (s'=4);
<> s=4 -> rateProcessing : (s'=0) + (rateA+rateB) : (s'=5);
<> s=5 -> 1 : true;
endmodule
label "error" = (s=5);
label "processB" = (s=3);

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examples/multiobjective/ma/simple/simple.csl
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multi(Pmax=? [ F s=3 ], Pmax=? [ F s=4 ])

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examples/multiobjective/ma/simple/simple.ma
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ma
module simple
s : [0..4];
[alpha] (s=0) -> 1 : (s' = 1);
[beta] (s=0) -> 0.8 : (s'=0) + 0.2 : (s'=2);
<> (s=1) -> 9 : (s'=0) + 1 : (s'=3);
<> (s=2) -> 12 : (s'=4);
<> (s>2) -> 1 : true;
endmodule

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examples/multiobjective/ma/stream/stream.ma
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ma
const int N; // num packages
const double inRate = 4;
const double processingRate = 4;
module streamingclient
s : [0..3]; // current state:
// 0: decide whether to start
// 1: buffering
// 2: running
// 3: success
n : [0..N]; // number of received packages
k : [0..N]; // number of processed packages
[buffer] s=0 & n<N & k=n -> 1 : (s'=1);
[buffer] s=0 & n<N & k<n -> 0.99: (s'=1) + 0.01 : (s'=2) & (k'=k+1);
[start] s=0 & k<n -> 1 : (s'=2) & (k'=k+1);
<> s=1 -> inRate : (n'=n+1) & (s'=0);
<> s=2 & n<N & k<n -> inRate : (n'=n+1) + processingRate : (k'=k+1);
<> s=2 & n<N & k=n -> inRate : (n'=n+1) + processingRate : (s'=0);
<> s=2 & n=N & k<n -> processingRate : (k'=k+1);
<> s=2 & n=N & k=N -> processingRate : (s'=3);
<> s=3 -> 1 : true;
endmodule
label "underrun" = (s=0 & k>0);
label "running" = (s=2);
label "done" = (s=3);
rewards "buffering"
s=1 : 1;
endrewards
rewards "numrestarts"
[start] k > 0 : 1;
endrewards

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examples/multiobjective/ma/stream/stream_bounded_pareto.csl
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multi(Pmax=? [ F<=3.5 "done" ], Pmax=? [ F<=1 s=2 ])

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examples/multiobjective/ma/stream/stream_mixed_pareto.csl
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multi(Pmax=? [ F<=2.5 s=2], R{"numrestarts"}min=? [ F "done"])
// best looking on stream50

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examples/multiobjective/ma/stream/stream_unbounded_pareto.csl
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multi(R{"initialbuffering"}min=? [ F "done" ], R{"numRestarts"}min=? [ F "done" ])

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examples/multiobjective/mdp/consensus/consensus2_3_2.nm
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// model of randomised consensus
mdp
const int N = 2; // num processes
const int MAX = 3; // num rounds (R)
const int K = 2; // Parameter for coins
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2)) & (p2=1 | r2<max(r1,r2));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2)) & (p2=2 | r2<max(r1,r2));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2)-1) & (p2=1 | r2<max(r1,r2)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2)-1) & (p2=2 | r2<max(r1,r2)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p1,
r1=r2,r2=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
endmodule
// coins 2 and 3 are of no use as there are not enough rounds afterwards to decide
// Labels
label "one_proc_err" = (s1=5 | s2=5);
label "one_coin_ok" = (c1=0);

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examples/multiobjective/mdp/consensus/consensus2_3_2_numerical.pctl
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multi(Pmax=? [ F "one_proc_err" ], P>=0.8916673903 [ G "one_coin_ok" ])

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examples/multiobjective/mdp/consensus/consensus2_3_2_pareto.pctl
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multi(Pmax=? [ F "one_proc_err" ], Pmax=? [ G "one_coin_ok" ])

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examples/multiobjective/mdp/consensus/consensus2_4_2.nm
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// model of randomised consensus
mdp
const int N = 2; // num processes
const int MAX = 4; // num rounds (R)
const int K = 2; // Parameter for coins
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2)) & (p2=1 | r2<max(r1,r2));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2)) & (p2=2 | r2<max(r1,r2));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2)-1) & (p2=1 | r2<max(r1,r2)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2)-1) & (p2=2 | r2<max(r1,r2)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
[coin3_s1_start] s1=2 & r1=3 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin3_s1_p1] s1=3 & r1=3 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin3_s1_p2] s1=3 & r1=3 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p1,
r1=r2,r2=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,coin3_s1_start=coin3_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,coin3_s1_p1=coin3_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2,coin3_s1_p2=coin3_s2_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
endmodule
// could do with renaming
module coin2_error
c2 : [0..1]; // 1 is the error state
v2 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin2_s1_p1] v2=0 -> (v2'=1);
[coin2_s2_p1] v2=0 -> (v2'=1);
[coin2_s1_p2] v2=0 -> (v2'=2);
[coin2_s2_p2] v2=0 -> (v2'=2);
// later values returned
[coin2_s1_p1] v2=1 -> true; // good behaviour
[coin2_s2_p1] v2=1 -> true; // good behaviour
[coin2_s1_p2] v2=2 -> true; // good behaviour
[coin2_s2_p2] v2=2 -> true; // good behaviour
[coin2_s1_p1] v2=2 -> (c2'=1); // error
[coin2_s2_p1] v2=2 -> (c2'=1); // error
[coin2_s1_p2] v2=1 -> (c2'=1); // error
[coin2_s2_p2] v2=1 -> (c2'=1); // error
endmodule
// coin 3 is of no use because of number of rounds
// Labels
label "one_proc_err" = (s1=5 | s2=5);
label "one_coin_ok" = (c1=0 | c2=0);

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examples/multiobjective/mdp/consensus/consensus2_4_2_numerical.pctl
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multi(Pmax=? [ F "one_proc_err" ], P>=0.9882640457 [ G "one_coin_ok" ])

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examples/multiobjective/mdp/consensus/consensus2_4_2_pareto.pctl
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multi(Pmax=? [ F "one_proc_err" ], Pmax=? [ G "one_coin_ok" ])

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examples/multiobjective/mdp/consensus/consensus2_5_2.nm
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// model of randomised consensus
mdp
const int N = 2; // num processes
const int MAX = 5; // num rounds (R)
const int K = 2; // Parameter for coins
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2)) & (p2=1 | r2<max(r1,r2));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2)) & (p2=2 | r2<max(r1,r2));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2)-1) & (p2=1 | r2<max(r1,r2)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2)-1) & (p2=2 | r2<max(r1,r2)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
[coin3_s1_start] s1=2 & r1=3 -> (s1'=3);
[coin4_s1_start] s1=2 & r1=4 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin3_s1_p1] s1=3 & r1=3 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin3_s1_p2] s1=3 & r1=3 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin4_s1_p1] s1=3 & r1=4 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin4_s1_p2] s1=3 & r1=4 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p1,
r1=r2,r2=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,coin3_s1_start=coin3_s2_start,coin4_s1_start=coin4_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,coin3_s1_p1=coin3_s2_p1,coin4_s1_p1=coin4_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2,coin3_s1_p2=coin3_s2_p2,coin4_s1_p2=coin4_s2_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
endmodule
// could do with renaming
module coin2_error
c2 : [0..1]; // 1 is the error state
v2 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin2_s1_p1] v2=0 -> (v2'=1);
[coin2_s2_p1] v2=0 -> (v2'=1);
[coin2_s1_p2] v2=0 -> (v2'=2);
[coin2_s2_p2] v2=0 -> (v2'=2);
// later values returned
[coin2_s1_p1] v2=1 -> true; // good behaviour
[coin2_s2_p1] v2=1 -> true; // good behaviour
[coin2_s1_p2] v2=2 -> true; // good behaviour
[coin2_s2_p2] v2=2 -> true; // good behaviour
[coin2_s1_p1] v2=2 -> (c2'=1); // error
[coin2_s2_p1] v2=2 -> (c2'=1); // error
[coin2_s1_p2] v2=1 -> (c2'=1); // error
[coin2_s2_p2] v2=1 -> (c2'=1); // error
endmodule
// could do with renaming
module coin3_error
c3 : [0..1]; // 1 is the error state
v3 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin3_s1_p1] v3=0 -> (v3'=1);
[coin3_s2_p1] v3=0 -> (v3'=1);
[coin3_s1_p2] v3=0 -> (v3'=2);
[coin3_s2_p2] v3=0 -> (v3'=2);
// later values returned
[coin3_s1_p1] v3=1 -> true; // good behaviour
[coin3_s2_p1] v3=1 -> true; // good behaviour
[coin3_s1_p2] v3=2 -> true; // good behaviour
[coin3_s2_p2] v3=2 -> true; // good behaviour
[coin3_s1_p1] v3=2 -> (c3'=1); // error
[coin3_s2_p1] v3=2 -> (c3'=1); // error
[coin3_s1_p2] v3=1 -> (c3'=1); // error
[coin3_s2_p2] v3=1 -> (c3'=1); // error
endmodule
// coin 4 is of no use because of number of rounds
// Labels
label "one_proc_err" = (s1=5 | s2=5);
label "one_coin_ok" = (c1=0 | c2=0 | c3=0);

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multi(Pmax=? [ F "one_proc_err" ], P>=0.9987286134 [ G "one_coin_ok" ])

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multi(Pmax=? [ F "one_proc_err" ], Pmax=? [ G "one_coin_ok" ])

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// model of randomised consensus
mdp
const int N = 3; // num processes
const int MAX = 3; // num rounds (R)
const int K = 2; // Parameter for coins
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2,r3)) & (p2=1 | r2<max(r1,r2,r3)) & (p3=1 | r3<max(r1,r2,r3));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2,r3)) & (p2=2 | r2<max(r1,r2,r3)) & (p3=2 | r3<max(r1,r2,r3));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2,r3)-1) & (p2=1 | r2<max(r1,r2,r3)-1) & (p3=1 | r3<max(r1,r2,r3)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2,r3)-1) & (p2=2 | r2<max(r1,r2,r3)-1) & (p3=2 | r3<max(r1,r2,r3)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p3,p3=p1,
r1=r2,r2=r3,r3=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2 ]
endmodule
module process3 = process1[ s1=s3,
p1=p3,p2=p1,p3=p2,
r1=r3,r2=r1,r3=r2,
coin1_s1_start=coin1_s3_start,coin2_s1_start=coin2_s3_start,
coin1_s1_p1=coin1_s3_p1,coin2_s1_p1=coin2_s3_p1,
coin1_s1_p2=coin1_s3_p2,coin2_s1_p2=coin2_s3_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s3_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
[coin1_s3_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s3_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s3_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s3_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
[coin1_s3_p2] v1=1 -> (c1'=1); // error
endmodule
// Labels
label "one_proc_err" = (s1=5 | s2=5 | s3=5);
label "one_coin_ok" = (c1=0);

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multi(Pmax=? [ F "one_proc_err" ], P>=0.7709112445 [ G "one_coin_ok" ])

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multi(Pmax=? [ F "one_proc_err" ], Pmax=? [ G "one_coin_ok" ])

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// model of randomised consensus
mdp
const int N = 3; // num processes
const int MAX = 4; // num rounds (R)
const int K = 2; // Parameter for coins
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2,r3)) & (p2=1 | r2<max(r1,r2,r3)) & (p3=1 | r3<max(r1,r2,r3));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2,r3)) & (p2=2 | r2<max(r1,r2,r3)) & (p3=2 | r3<max(r1,r2,r3));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2,r3)-1) & (p2=1 | r2<max(r1,r2,r3)-1) & (p3=1 | r3<max(r1,r2,r3)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2,r3)-1) & (p2=2 | r2<max(r1,r2,r3)-1) & (p3=2 | r3<max(r1,r2,r3)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
[coin3_s1_start] s1=2 & r1=3 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin3_s1_p1] s1=3 & r1=3 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin3_s1_p2] s1=3 & r1=3 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p3,p3=p1,
r1=r2,r2=r3,r3=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,coin3_s1_start=coin3_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,coin3_s1_p1=coin3_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2,coin3_s1_p2=coin3_s2_p2 ]
endmodule
module process3 = process1[ s1=s3,
p1=p3,p2=p1,p3=p2,
r1=r3,r2=r1,r3=r2,
coin1_s1_start=coin1_s3_start,coin2_s1_start=coin2_s3_start,coin3_s1_start=coin3_s3_start,
coin1_s1_p1=coin1_s3_p1,coin2_s1_p1=coin2_s3_p1,coin3_s1_p1=coin3_s3_p1,
coin1_s1_p2=coin1_s3_p2,coin2_s1_p2=coin2_s3_p2,coin3_s1_p2=coin3_s3_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s3_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
[coin1_s3_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s3_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s3_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s3_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
[coin1_s3_p2] v1=1 -> (c1'=1); // error
endmodule
module coin2_error
c2 : [0..1]; // 1 is the error state
v2 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin2_s1_p1] v2=0 -> (v2'=1);
[coin2_s2_p1] v2=0 -> (v2'=1);
[coin2_s3_p1] v2=0 -> (v2'=1);
[coin2_s1_p2] v2=0 -> (v2'=2);
[coin2_s2_p2] v2=0 -> (v2'=2);
[coin2_s3_p2] v2=0 -> (v2'=2);
// later values returned
[coin2_s1_p1] v2=1 -> true; // good behaviour
[coin2_s2_p1] v2=1 -> true; // good behaviour
[coin2_s3_p1] v2=1 -> true; // good behaviour
[coin2_s1_p2] v2=2 -> true; // good behaviour
[coin2_s2_p2] v2=2 -> true; // good behaviour
[coin2_s3_p2] v2=2 -> true; // good behaviour
[coin2_s1_p1] v2=2 -> (c2'=1); // error
[coin2_s2_p1] v2=2 -> (c2'=1); // error
[coin2_s3_p1] v2=2 -> (c2'=1); // error
[coin2_s1_p2] v2=1 -> (c2'=1); // error
[coin2_s2_p2] v2=1 -> (c2'=1); // error
[coin2_s3_p2] v2=1 -> (c2'=1); // error
endmodule
// Labels
label "one_proc_err" = (s1=5 | s2=5 | s3=5);
label "one_coin_ok" = (c1=0 | c2=0);

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multi(Pmax=? [ F "one_proc_err" ], P>=0.9475183421 [ G "one_coin_ok" ])

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multi(Pmax=? [ F "one_proc_err" ], Pmax=? [ G "one_coin_ok" ])

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// model of randomised consensus
mdp
const int N = 3; // num processes
const int MAX = 5; // num rounds (R)
const int K = 2; // Parameter for coins
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2,r3)) & (p2=1 | r2<max(r1,r2,r3)) & (p3=1 | r3<max(r1,r2,r3));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2,r3)) & (p2=2 | r2<max(r1,r2,r3)) & (p3=2 | r3<max(r1,r2,r3));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2,r3)-1) & (p2=1 | r2<max(r1,r2,r3)-1) & (p3=1 | r3<max(r1,r2,r3)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2,r3)-1) & (p2=2 | r2<max(r1,r2,r3)-1) & (p3=2 | r3<max(r1,r2,r3)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
[coin3_s1_start] s1=2 & r1=3 -> (s1'=3);
[coin4_s1_start] s1=2 & r1=4 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin3_s1_p1] s1=3 & r1=3 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin3_s1_p2] s1=3 & r1=3 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin4_s1_p1] s1=3 & r1=4 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin4_s1_p2] s1=3 & r1=4 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p3,p3=p1,
r1=r2,r2=r3,r3=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,coin3_s1_start=coin3_s2_start,coin4_s1_start=coin4_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,coin3_s1_p1=coin3_s2_p1,coin4_s1_p1=coin4_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2,coin3_s1_p2=coin3_s2_p2,coin4_s1_p2=coin4_s2_p2 ]
endmodule
module process3 = process1[ s1=s3,
p1=p3,p2=p1,p3=p2,
r1=r3,r2=r1,r3=r2,
coin1_s1_start=coin1_s3_start,coin2_s1_start=coin2_s3_start,coin3_s1_start=coin3_s3_start,coin4_s1_start=coin4_s3_start,
coin1_s1_p1=coin1_s3_p1,coin2_s1_p1=coin2_s3_p1,coin3_s1_p1=coin3_s3_p1,coin4_s1_p1=coin4_s3_p1,
coin1_s1_p2=coin1_s3_p2,coin2_s1_p2=coin2_s3_p2,coin3_s1_p2=coin3_s3_p2,coin4_s1_p2=coin4_s3_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s3_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
[coin1_s3_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s3_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s3_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s3_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
[coin1_s3_p2] v1=1 -> (c1'=1); // error
endmodule
module coin2_error
c2 : [0..1]; // 1 is the error state
v2 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin2_s1_p1] v2=0 -> (v2'=1);
[coin2_s2_p1] v2=0 -> (v2'=1);
[coin2_s3_p1] v2=0 -> (v2'=1);
[coin2_s1_p2] v2=0 -> (v2'=2);
[coin2_s2_p2] v2=0 -> (v2'=2);
[coin2_s3_p2] v2=0 -> (v2'=2);
// later values returned
[coin2_s1_p1] v2=1 -> true; // good behaviour
[coin2_s2_p1] v2=1 -> true; // good behaviour
[coin2_s3_p1] v2=1 -> true; // good behaviour
[coin2_s1_p2] v2=2 -> true; // good behaviour
[coin2_s2_p2] v2=2 -> true; // good behaviour
[coin2_s3_p2] v2=2 -> true; // good behaviour
[coin2_s1_p1] v2=2 -> (c2'=1); // error
[coin2_s2_p1] v2=2 -> (c2'=1); // error
[coin2_s3_p1] v2=2 -> (c2'=1); // error
[coin2_s1_p2] v2=1 -> (c2'=1); // error
[coin2_s2_p2] v2=1 -> (c2'=1); // error
[coin2_s3_p2] v2=1 -> (c2'=1); // error
endmodule
module coin3_error
c3 : [0..1]; // 1 is the error state
v3 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin3_s1_p1] v3=0 -> (v3'=1);
[coin3_s2_p1] v3=0 -> (v3'=1);
[coin3_s3_p1] v3=0 -> (v3'=1);
[coin3_s1_p2] v3=0 -> (v3'=2);
[coin3_s2_p2] v3=0 -> (v3'=2);
[coin3_s3_p2] v3=0 -> (v3'=2);
// later values returned
[coin3_s1_p1] v3=1 -> true; // good behaviour
[coin3_s2_p1] v3=1 -> true; // good behaviour
[coin3_s3_p1] v3=1 -> true; // good behaviour
[coin3_s1_p2] v3=2 -> true; // good behaviour
[coin3_s2_p2] v3=2 -> true; // good behaviour
[coin3_s3_p2] v3=2 -> true; // good behaviour
[coin3_s1_p1] v3=2 -> (c3'=1); // error
[coin3_s2_p1] v3=2 -> (c3'=1); // error
[coin3_s3_p1] v3=2 -> (c3'=1); // error
[coin3_s1_p2] v3=1 -> (c3'=1); // error
[coin3_s2_p2] v3=1 -> (c3'=1); // error
[coin3_s3_p2] v3=1 -> (c3'=1); // error
endmodule
// Labels
label "one_proc_err" = (s1=5 | s2=5 | s3=5);
label "one_coin_ok" = (c1=0 | c2=0 | c3=0);

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multi(Pmax=? [ F "one_proc_err" ], P>=0.9879770423 [ G "one_coin_ok" ])

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multi(Pmax=? [ F "one_proc_err" ], Pmax=? [ G "one_coin_ok" ])

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// model of randomised consensus
mdp
const int N = 2; // num processes
const int MAX = 3; // num rounds (R)
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2)) & (p2=1 | r2<max(r1,r2));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2)) & (p2=2 | r2<max(r1,r2));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2)-1) & (p2=1 | r2<max(r1,r2)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2)-1) & (p2=2 | r2<max(r1,r2)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p1,
r1=r2,r2=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
endmodule
// coins 2 and 3 are of no use as there are not enough rounds afterwards to decide
// Labels
label "one_proc_err" = (s1=5 | s2=5);
label "one_coin_ok" = (c1=0);

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// model of randomised consensus
mdp
const int N = 2; // num processes
const int MAX = 4; // num rounds (R)
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2)) & (p2=1 | r2<max(r1,r2));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2)) & (p2=2 | r2<max(r1,r2));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2)-1) & (p2=1 | r2<max(r1,r2)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2)-1) & (p2=2 | r2<max(r1,r2)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
[coin3_s1_start] s1=2 & r1=3 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin3_s1_p1] s1=3 & r1=3 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin3_s1_p2] s1=3 & r1=3 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p1,
r1=r2,r2=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,coin3_s1_start=coin3_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,coin3_s1_p1=coin3_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2,coin3_s1_p2=coin3_s2_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
endmodule
// could do with renaming
module coin2_error
c2 : [0..1]; // 1 is the error state
v2 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin2_s1_p1] v2=0 -> (v2'=1);
[coin2_s2_p1] v2=0 -> (v2'=1);
[coin2_s1_p2] v2=0 -> (v2'=2);
[coin2_s2_p2] v2=0 -> (v2'=2);
// later values returned
[coin2_s1_p1] v2=1 -> true; // good behaviour
[coin2_s2_p1] v2=1 -> true; // good behaviour
[coin2_s1_p2] v2=2 -> true; // good behaviour
[coin2_s2_p2] v2=2 -> true; // good behaviour
[coin2_s1_p1] v2=2 -> (c2'=1); // error
[coin2_s2_p1] v2=2 -> (c2'=1); // error
[coin2_s1_p2] v2=1 -> (c2'=1); // error
[coin2_s2_p2] v2=1 -> (c2'=1); // error
endmodule
// coin 3 is of no use because of number of rounds
// Labels
label "one_proc_err" = (s1=5 | s2=5);
label "one_coin_ok" = (c1=0 | c2=0);

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// model of randomised consensus
mdp
const int N = 2; // num processes
const int MAX = 5; // num rounds (R)
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2)) & (p2=1 | r2<max(r1,r2));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2)) & (p2=2 | r2<max(r1,r2));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2)-1) & (p2=1 | r2<max(r1,r2)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2)-1) & (p2=2 | r2<max(r1,r2)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
[coin3_s1_start] s1=2 & r1=3 -> (s1'=3);
[coin4_s1_start] s1=2 & r1=4 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin3_s1_p1] s1=3 & r1=3 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin3_s1_p2] s1=3 & r1=3 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin4_s1_p1] s1=3 & r1=4 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin4_s1_p2] s1=3 & r1=4 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p1,
r1=r2,r2=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,coin3_s1_start=coin3_s2_start,coin4_s1_start=coin4_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,coin3_s1_p1=coin3_s2_p1,coin4_s1_p1=coin4_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2,coin3_s1_p2=coin3_s2_p2,coin4_s1_p2=coin4_s2_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
endmodule
// could do with renaming
module coin2_error
c2 : [0..1]; // 1 is the error state
v2 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin2_s1_p1] v2=0 -> (v2'=1);
[coin2_s2_p1] v2=0 -> (v2'=1);
[coin2_s1_p2] v2=0 -> (v2'=2);
[coin2_s2_p2] v2=0 -> (v2'=2);
// later values returned
[coin2_s1_p1] v2=1 -> true; // good behaviour
[coin2_s2_p1] v2=1 -> true; // good behaviour
[coin2_s1_p2] v2=2 -> true; // good behaviour
[coin2_s2_p2] v2=2 -> true; // good behaviour
[coin2_s1_p1] v2=2 -> (c2'=1); // error
[coin2_s2_p1] v2=2 -> (c2'=1); // error
[coin2_s1_p2] v2=1 -> (c2'=1); // error
[coin2_s2_p2] v2=1 -> (c2'=1); // error
endmodule
// could do with renaming
module coin3_error
c3 : [0..1]; // 1 is the error state
v3 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin3_s1_p1] v3=0 -> (v3'=1);
[coin3_s2_p1] v3=0 -> (v3'=1);
[coin3_s1_p2] v3=0 -> (v3'=2);
[coin3_s2_p2] v3=0 -> (v3'=2);
// later values returned
[coin3_s1_p1] v3=1 -> true; // good behaviour
[coin3_s2_p1] v3=1 -> true; // good behaviour
[coin3_s1_p2] v3=2 -> true; // good behaviour
[coin3_s2_p2] v3=2 -> true; // good behaviour
[coin3_s1_p1] v3=2 -> (c3'=1); // error
[coin3_s2_p1] v3=2 -> (c3'=1); // error
[coin3_s1_p2] v3=1 -> (c3'=1); // error
[coin3_s2_p2] v3=1 -> (c3'=1); // error
endmodule
// coin 4 is of no use because of number of rounds
// Labels
label "one_proc_err" = (s1=5 | s2=5);
label "one_coin_ok" = (c1=0 | c2=0 | c3=0);

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// model of randomised consensus
mdp
const int N = 3; // num processes
const int MAX = 3; // num rounds (R)
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2,r3)) & (p2=1 | r2<max(r1,r2,r3)) & (p3=1 | r3<max(r1,r2,r3));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2,r3)) & (p2=2 | r2<max(r1,r2,r3)) & (p3=2 | r3<max(r1,r2,r3));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2,r3)-1) & (p2=1 | r2<max(r1,r2,r3)-1) & (p3=1 | r3<max(r1,r2,r3)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2,r3)-1) & (p2=2 | r2<max(r1,r2,r3)-1) & (p3=2 | r3<max(r1,r2,r3)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p3,p3=p1,
r1=r2,r2=r3,r3=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2 ]
endmodule
module process3 = process1[ s1=s3,
p1=p3,p2=p1,p3=p2,
r1=r3,r2=r1,r3=r2,
coin1_s1_start=coin1_s3_start,coin2_s1_start=coin2_s3_start,
coin1_s1_p1=coin1_s3_p1,coin2_s1_p1=coin2_s3_p1,
coin1_s1_p2=coin1_s3_p2,coin2_s1_p2=coin2_s3_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s3_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
[coin1_s3_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s3_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s3_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s3_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
[coin1_s3_p2] v1=1 -> (c1'=1); // error
endmodule
// Labels
label "one_proc_err" = (s1=5 | s2=5 | s3=5);
label "one_coin_ok" = (c1=0);

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// model of randomised consensus
mdp
const int N = 3; // num processes
const int MAX = 4; // num rounds (R)
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2,r3)) & (p2=1 | r2<max(r1,r2,r3)) & (p3=1 | r3<max(r1,r2,r3));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2,r3)) & (p2=2 | r2<max(r1,r2,r3)) & (p3=2 | r3<max(r1,r2,r3));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2,r3)-1) & (p2=1 | r2<max(r1,r2,r3)-1) & (p3=1 | r3<max(r1,r2,r3)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2,r3)-1) & (p2=2 | r2<max(r1,r2,r3)-1) & (p3=2 | r3<max(r1,r2,r3)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
[coin3_s1_start] s1=2 & r1=3 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin3_s1_p1] s1=3 & r1=3 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin3_s1_p2] s1=3 & r1=3 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p3,p3=p1,
r1=r2,r2=r3,r3=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,coin3_s1_start=coin3_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,coin3_s1_p1=coin3_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2,coin3_s1_p2=coin3_s2_p2 ]
endmodule
module process3 = process1[ s1=s3,
p1=p3,p2=p1,p3=p2,
r1=r3,r2=r1,r3=r2,
coin1_s1_start=coin1_s3_start,coin2_s1_start=coin2_s3_start,coin3_s1_start=coin3_s3_start,
coin1_s1_p1=coin1_s3_p1,coin2_s1_p1=coin2_s3_p1,coin3_s1_p1=coin3_s3_p1,
coin1_s1_p2=coin1_s3_p2,coin2_s1_p2=coin2_s3_p2,coin3_s1_p2=coin3_s3_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s3_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
[coin1_s3_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s3_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s3_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s3_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
[coin1_s3_p2] v1=1 -> (c1'=1); // error
endmodule
module coin2_error
c2 : [0..1]; // 1 is the error state
v2 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin2_s1_p1] v2=0 -> (v2'=1);
[coin2_s2_p1] v2=0 -> (v2'=1);
[coin2_s3_p1] v2=0 -> (v2'=1);
[coin2_s1_p2] v2=0 -> (v2'=2);
[coin2_s2_p2] v2=0 -> (v2'=2);
[coin2_s3_p2] v2=0 -> (v2'=2);
// later values returned
[coin2_s1_p1] v2=1 -> true; // good behaviour
[coin2_s2_p1] v2=1 -> true; // good behaviour
[coin2_s3_p1] v2=1 -> true; // good behaviour
[coin2_s1_p2] v2=2 -> true; // good behaviour
[coin2_s2_p2] v2=2 -> true; // good behaviour
[coin2_s3_p2] v2=2 -> true; // good behaviour
[coin2_s1_p1] v2=2 -> (c2'=1); // error
[coin2_s2_p1] v2=2 -> (c2'=1); // error
[coin2_s3_p1] v2=2 -> (c2'=1); // error
[coin2_s1_p2] v2=1 -> (c2'=1); // error
[coin2_s2_p2] v2=1 -> (c2'=1); // error
[coin2_s3_p2] v2=1 -> (c2'=1); // error
endmodule
// Labels
label "one_proc_err" = (s1=5 | s2=5 | s3=5);
label "one_coin_ok" = (c1=0 | c2=0);

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// model of randomised consensus
mdp
const int N = 3; // num processes
const int MAX = 5; // num rounds (R)
// need to turn these into local copies later so the reading phase is complete?
formula leaders_agree1 = (p1=1 | r1<max(r1,r2,r3)) & (p2=1 | r2<max(r1,r2,r3)) & (p3=1 | r3<max(r1,r2,r3));
formula leaders_agree2 = (p1=2 | r1<max(r1,r2,r3)) & (p2=2 | r2<max(r1,r2,r3)) & (p3=2 | r3<max(r1,r2,r3));
formula decide1 = leaders_agree1 & (p1=1 | r1<max(r1,r2,r3)-1) & (p2=1 | r2<max(r1,r2,r3)-1) & (p3=1 | r3<max(r1,r2,r3)-1);
formula decide2 = leaders_agree2 & (p1=2 | r1<max(r1,r2,r3)-1) & (p2=2 | r2<max(r1,r2,r3)-1) & (p3=2 | r3<max(r1,r2,r3)-1);
module process1
s1 : [0..5]; // local state
// 0 initialise/read registers
// 1 finish reading registers (make a decision)
// 1 warn of change
// 2 enter shared coin protocol
// 4 finished
// 5 error (reached max round and cannot decide)
r1 : [0..MAX]; // round of the process
p1 : [0..2]; // preference (0 corresponds to null)
// nondeterministic choice as to initial preference
[] s1=0 & r1=0 -> (p1'=1) & (r1'=1);
[] s1=0 & r1=0 -> (p1'=2) & (r1'=1);
// read registers (currently does nothing because read vs from other processes
[] s1=0 & r1>0 & r1<=MAX -> (s1'=1);
// maxke a decision
[] s1=1 & decide1 -> (s1'=4) & (p1'=1);
[] s1=1 & decide2 -> (s1'=4) & (p1'=2);
[] s1=1 & r1<MAX & leaders_agree1 & !decide1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[] s1=1 & r1<MAX & leaders_agree2 & !decide2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[] s1=1 & r1<MAX & !(leaders_agree1 | leaders_agree2) -> (s1'=2) & (p1'=0);
[] s1=1 & r1=MAX & !(decide1 | decide2) -> (s1'=5); // run out of rounds so error
// enter the coin procotol for the current round
[coin1_s1_start] s1=2 & r1=1 -> (s1'=3);
[coin2_s1_start] s1=2 & r1=2 -> (s1'=3);
[coin3_s1_start] s1=2 & r1=3 -> (s1'=3);
[coin4_s1_start] s1=2 & r1=4 -> (s1'=3);
// get response from the coin protocol
[coin1_s1_p1] s1=3 & r1=1 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin1_s1_p2] s1=3 & r1=1 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin2_s1_p1] s1=3 & r1=2 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin2_s1_p2] s1=3 & r1=2 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin3_s1_p1] s1=3 & r1=3 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin3_s1_p2] s1=3 & r1=3 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
[coin4_s1_p1] s1=3 & r1=4 -> (s1'=0) & (p1'=1) & (r1'=r1+1);
[coin4_s1_p2] s1=3 & r1=4 -> (s1'=0) & (p1'=2) & (r1'=r1+1);
// done so loop
[done] s1>=4 -> true;
endmodule
module process2 = process1[ s1=s2,
p1=p2,p2=p3,p3=p1,
r1=r2,r2=r3,r3=r1,
coin1_s1_start=coin1_s2_start,coin2_s1_start=coin2_s2_start,coin3_s1_start=coin3_s2_start,coin4_s1_start=coin4_s2_start,
coin1_s1_p1=coin1_s2_p1,coin2_s1_p1=coin2_s2_p1,coin3_s1_p1=coin3_s2_p1,coin4_s1_p1=coin4_s2_p1,
coin1_s1_p2=coin1_s2_p2,coin2_s1_p2=coin2_s2_p2,coin3_s1_p2=coin3_s2_p2,coin4_s1_p2=coin4_s2_p2 ]
endmodule
module process3 = process1[ s1=s3,
p1=p3,p2=p1,p3=p2,
r1=r3,r2=r1,r3=r2,
coin1_s1_start=coin1_s3_start,coin2_s1_start=coin2_s3_start,coin3_s1_start=coin3_s3_start,coin4_s1_start=coin4_s3_start,
coin1_s1_p1=coin1_s3_p1,coin2_s1_p1=coin2_s3_p1,coin3_s1_p1=coin3_s3_p1,coin4_s1_p1=coin4_s3_p1,
coin1_s1_p2=coin1_s3_p2,coin2_s1_p2=coin2_s3_p2,coin3_s1_p2=coin3_s3_p2,coin4_s1_p2=coin4_s3_p2 ]
endmodule
module coin1_error
c1 : [0..1]; // 1 is the error state
v1 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin1_s1_p1] v1=0 -> (v1'=1);
[coin1_s2_p1] v1=0 -> (v1'=1);
[coin1_s3_p1] v1=0 -> (v1'=1);
[coin1_s1_p2] v1=0 -> (v1'=2);
[coin1_s2_p2] v1=0 -> (v1'=2);
[coin1_s3_p2] v1=0 -> (v1'=2);
// later values returned
[coin1_s1_p1] v1=1 -> true; // good behaviour
[coin1_s2_p1] v1=1 -> true; // good behaviour
[coin1_s3_p1] v1=1 -> true; // good behaviour
[coin1_s1_p2] v1=2 -> true; // good behaviour
[coin1_s2_p2] v1=2 -> true; // good behaviour
[coin1_s3_p2] v1=2 -> true; // good behaviour
[coin1_s1_p1] v1=2 -> (c1'=1); // error
[coin1_s2_p1] v1=2 -> (c1'=1); // error
[coin1_s3_p1] v1=2 -> (c1'=1); // error
[coin1_s1_p2] v1=1 -> (c1'=1); // error
[coin1_s2_p2] v1=1 -> (c1'=1); // error
[coin1_s3_p2] v1=1 -> (c1'=1); // error
endmodule
module coin2_error
c2 : [0..1]; // 1 is the error state
v2 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin2_s1_p1] v2=0 -> (v2'=1);
[coin2_s2_p1] v2=0 -> (v2'=1);
[coin2_s3_p1] v2=0 -> (v2'=1);
[coin2_s1_p2] v2=0 -> (v2'=2);
[coin2_s2_p2] v2=0 -> (v2'=2);
[coin2_s3_p2] v2=0 -> (v2'=2);
// later values returned
[coin2_s1_p1] v2=1 -> true; // good behaviour
[coin2_s2_p1] v2=1 -> true; // good behaviour
[coin2_s3_p1] v2=1 -> true; // good behaviour
[coin2_s1_p2] v2=2 -> true; // good behaviour
[coin2_s2_p2] v2=2 -> true; // good behaviour
[coin2_s3_p2] v2=2 -> true; // good behaviour
[coin2_s1_p1] v2=2 -> (c2'=1); // error
[coin2_s2_p1] v2=2 -> (c2'=1); // error
[coin2_s3_p1] v2=2 -> (c2'=1); // error
[coin2_s1_p2] v2=1 -> (c2'=1); // error
[coin2_s2_p2] v2=1 -> (c2'=1); // error
[coin2_s3_p2] v2=1 -> (c2'=1); // error
endmodule
module coin3_error
c3 : [0..1]; // 1 is the error state
v3 : [0..2]; // value of the coin returned the first time
// first returned value (any processes)
[coin3_s1_p1] v3=0 -> (v3'=1);
[coin3_s2_p1] v3=0 -> (v3'=1);
[coin3_s3_p1] v3=0 -> (v3'=1);
[coin3_s1_p2] v3=0 -> (v3'=2);
[coin3_s2_p2] v3=0 -> (v3'=2);
[coin3_s3_p2] v3=0 -> (v3'=2);
// later values returned
[coin3_s1_p1] v3=1 -> true; // good behaviour
[coin3_s2_p1] v3=1 -> true; // good behaviour
[coin3_s3_p1] v3=1 -> true; // good behaviour
[coin3_s1_p2] v3=2 -> true; // good behaviour
[coin3_s2_p2] v3=2 -> true; // good behaviour
[coin3_s3_p2] v3=2 -> true; // good behaviour
[coin3_s1_p1] v3=2 -> (c3'=1); // error
[coin3_s2_p1] v3=2 -> (c3'=1); // error
[coin3_s3_p1] v3=2 -> (c3'=1); // error
[coin3_s1_p2] v3=1 -> (c3'=1); // error
[coin3_s2_p2] v3=1 -> (c3'=1); // error
[coin3_s3_p2] v3=1 -> (c3'=1); // error
endmodule
// Labels
label "one_proc_err" = (s1=5 | s2=5 | s3=5);
label "one_coin_ok" = (c1=0 | c2=0 | c3=0);

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// Parameter K for coins
const int K;
// Max probability of component (coins) violating assumption property (checked separately)
const double p_coin_fail =
N=2 ? (
K=2 ? 0.10833260973166493 :
K=12 ? 0.04164301267240658 :
K=20 ? 0.01249126244810821 :
0 ) :
N=3 ? (
K=2 ? 0.22908875545788154 :
K=4 ? 0.12450138796380239 :
K=8 ? 0.06248479880890645 :
K=12 ? 0.04164365757451993 :
K=16 ? 0.031218839562495382 :
K=20 ? 0.024960596483605935 :
0 ) : 0;
// Probability bound for assumption, derived from above
const double p_one_coin_ok = 1 - pow(p_coin_fail, MAX-2);
// Assume-guarantee check via multi-objective (using ASYM rule)
"num_ag": multi(Pmax=? [ F "one_proc_err" ], P>=p_one_coin_ok [ G "one_coin_ok" ])
// Pareto query for assume-guarantee check
"pareto": multi(Pmax=? [ F "one_proc_err" ], Pmax=? [ G "one_coin_ok" ])

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// power manager example
mdp
const int QMAX =2; // max queue size
// to model the pm making a choice and then a move being made we need
// two clock ticks for each transition
// first the pm decides tick1 and then the system moves tick2
module timer
c : [0..1];
[tick1] c=0 -> (c'=1);
[tick2] c=1 -> (c'=0);
endmodule
//-------------------------------------------------------------------------
// POWER MANAGER
module PM
pm : [0..4] init 4;
// 0 - go to active
// 1 - go to idle
// 2 - go to idlelp
// 3 - go to stby
// 4 - go to sleep
[tick1] true -> (pm'=0);
[tick1] true -> (pm'=1);
[tick1] true -> (pm'=2);
[tick1] true -> (pm'=3);
[tick1] true -> (pm'=4);
endmodule
//-------------------------------------------------------------------------
// SERVICE REQUESTER
module SR
sr : [0..1] init 0;
// 0 idle
// 1 1req
[tick2] sr=0 -> 0.898: (sr'=0) + 0.102: (sr'=1);
[tick2] sr=1 -> 0.454: (sr'=0) + 0.546: (sr'=1);
endmodule
//-------------------------------------------------------------------------
// SERVICE PROVIDER
module SP
sp : [0..10] init 9;
// 0 active
// 1 idle
// 2 active_idlelp
// 3 idlelp
// 4 idlelp_active
// 5 active_stby
// 6 stby
// 7 stby_active
// 8 active_sleep
// 9 sleep
// 10 sleep_active
// states where PM has no control (transient states)
[tick2] sp=2 -> 0.75 : (sp'=2) + 0.25 : (sp'=3); // active_idlelp
[tick2] sp=4 -> 0.25 : (sp'=0) + 0.75 : (sp'=4); // idlelp_active
[tick2] sp=5 -> 0.995 : (sp'=5) + 0.005 : (sp'=6); // active_stby
[tick2] sp=7 -> 0.005 : (sp'=0) + 0.995 : (sp'=7); // stby_active
[tick2] sp=8 -> 0.9983 : (sp'=8) + 0.0017 : (sp'=9); // active_sleep
[tick2] sp=10 -> 0.0017 : (sp'=0) + 0.9983 : (sp'=10); // sleep_active
// states where PM has control
// goto_active
[tick2] sp=0 & pm=0 -> (sp'=0); // active
[tick2] sp=1 & pm=0 -> (sp'=0); // idle
[tick2] sp=3 & pm=0 -> (sp'=4); // idlelp
[tick2] sp=6 & pm=0 -> (sp'=7); // stby
[tick2] sp=9 & pm=0 -> (sp'=10); // sleep
// goto_idle
[tick2] sp=0 & pm=1 -> (sp'=1); // active
[tick2] sp=1 & pm=1 -> (sp'=1); // idle
[tick2] sp=3 & pm=1 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=1 -> (sp'=6); // stby
[tick2] sp=9 & pm=1 -> (sp'=9); // sleep
// goto_idlelp
[tick2] sp=0 & pm=2 -> (sp'=2); // active
[tick2] sp=1 & pm=2 -> (sp'=2); // idle
[tick2] sp=3 & pm=2 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=2 -> (sp'=6); // stby
[tick2] sp=9 & pm=2 -> (sp'=9); // sleep
// goto_stby
[tick2] sp=0 & pm=3 -> (sp'=5); // active
[tick2] sp=1 & pm=3 -> (sp'=5); // idle
[tick2] sp=3 & pm=3 -> (sp'=5); // idlelp
[tick2] sp=6 & pm=3 -> (sp'=6); // stby
[tick2] sp=9 & pm=3 -> (sp'=9); // sleep
// goto_sleep
[tick2] sp=0 & pm=4 -> (sp'=8); // active
[tick2] sp=1 & pm=4 -> (sp'=8); // idle
[tick2] sp=3 & pm=4 -> (sp'=8); // idlelp
[tick2] sp=6 & pm=4 -> (sp'=8); // stby
[tick2] sp=9 & pm=4 -> (sp'=9); // sleep
endmodule
//-------------------------------------------------------------------------
// SQ
module SQ
q : [0..QMAX] init 0;
// serve if busy
[tick2] sr=0 & sp=0 -> (q'=max(q-1,0));
[tick2] sr=1 & sp=0 -> (q'=q);
// otherwise do nothing
[tick2] sr=0 & sp>0 -> (q'=q);
[tick2] sr=1 & sp>0 -> (q'=min(q+1,QMAX));
endmodule
//-------------------------------------------------------------------------
//rewards "time"
// [tick2] bat=1 : 1;
//endrewards
rewards "power"
[tick2] sp=0 & c=1 : 2.5;
[tick2] sp=1 & c=1 : 1.5;
[tick2] sp=2 & c=1 : 2.5;
[tick2] sp=3 & c=1 : 0.8;
[tick2] sp=4 & c=1 : 2.5;
[tick2] sp=5 & c=1 : 2.5;
[tick2] sp=6 & c=1 : 0.3;
[tick2] sp=7 & c=1 : 2.5;
[tick2] sp=8 & c=1 : 2.5;
[tick2] sp=9 & c=1 : 0.1;
[tick2] sp=10 & c=1 : 2.5;
endrewards
// is an instantaneous property but I suppose we can look at average size
// i.e. divide by the expected number of time steps
rewards "queue"
[tick2] c=1 : q;
endrewards
rewards "lost"
[tick2] sr=1 & sp>0 & q=2 : 1;
endrewards

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examples/multiobjective/mdp/dpm/dpm100_numerical.pctl
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multi(R{"power"}min=? [ C<=100 ], R{"queue"}<=70 [ C<=100 ])
// Note: The property file from http://www.prismmodelchecker.org/files/atva12mo/ does not provide a threshold for the second objective.
// We pick a threshold that intersects the pareto curve.

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examples/multiobjective/mdp/dpm/dpm100_pareto.pctl
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multi(R{"power"}min=? [ C<=100 ], R{"queue"}min=? [ C<=100 ])

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examples/multiobjective/mdp/dpm/dpm200.nm
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// power manager example
mdp
const int QMAX =2; // max queue size
// to model the pm making a choice and then a move being made we need
// two clock ticks for each transition
// first the pm decides tick1 and then the system moves tick2
module timer
c : [0..1];
[tick1] c=0 -> (c'=1);
[tick2] c=1 -> (c'=0);
endmodule
//-------------------------------------------------------------------------
// POWER MANAGER
module PM
pm : [0..4] init 4;
// 0 - go to active
// 1 - go to idle
// 2 - go to idlelp
// 3 - go to stby
// 4 - go to sleep
[tick1] true -> (pm'=0);
[tick1] true -> (pm'=1);
[tick1] true -> (pm'=2);
[tick1] true -> (pm'=3);
[tick1] true -> (pm'=4);
endmodule
//-------------------------------------------------------------------------
// SERVICE REQUESTER
module SR
sr : [0..1] init 0;
// 0 idle
// 1 1req
[tick2] sr=0 -> 0.898: (sr'=0) + 0.102: (sr'=1);
[tick2] sr=1 -> 0.454: (sr'=0) + 0.546: (sr'=1);
endmodule
//-------------------------------------------------------------------------
// SERVICE PROVIDER
module SP
sp : [0..10] init 9;
// 0 active
// 1 idle
// 2 active_idlelp
// 3 idlelp
// 4 idlelp_active
// 5 active_stby
// 6 stby
// 7 stby_active
// 8 active_sleep
// 9 sleep
// 10 sleep_active
// states where PM has no control (transient states)
[tick2] sp=2 -> 0.75 : (sp'=2) + 0.25 : (sp'=3); // active_idlelp
[tick2] sp=4 -> 0.25 : (sp'=0) + 0.75 : (sp'=4); // idlelp_active
[tick2] sp=5 -> 0.995 : (sp'=5) + 0.005 : (sp'=6); // active_stby
[tick2] sp=7 -> 0.005 : (sp'=0) + 0.995 : (sp'=7); // stby_active
[tick2] sp=8 -> 0.9983 : (sp'=8) + 0.0017 : (sp'=9); // active_sleep
[tick2] sp=10 -> 0.0017 : (sp'=0) + 0.9983 : (sp'=10); // sleep_active
// states where PM has control
// goto_active
[tick2] sp=0 & pm=0 -> (sp'=0); // active
[tick2] sp=1 & pm=0 -> (sp'=0); // idle
[tick2] sp=3 & pm=0 -> (sp'=4); // idlelp
[tick2] sp=6 & pm=0 -> (sp'=7); // stby
[tick2] sp=9 & pm=0 -> (sp'=10); // sleep
// goto_idle
[tick2] sp=0 & pm=1 -> (sp'=1); // active
[tick2] sp=1 & pm=1 -> (sp'=1); // idle
[tick2] sp=3 & pm=1 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=1 -> (sp'=6); // stby
[tick2] sp=9 & pm=1 -> (sp'=9); // sleep
// goto_idlelp
[tick2] sp=0 & pm=2 -> (sp'=2); // active
[tick2] sp=1 & pm=2 -> (sp'=2); // idle
[tick2] sp=3 & pm=2 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=2 -> (sp'=6); // stby
[tick2] sp=9 & pm=2 -> (sp'=9); // sleep
// goto_stby
[tick2] sp=0 & pm=3 -> (sp'=5); // active
[tick2] sp=1 & pm=3 -> (sp'=5); // idle
[tick2] sp=3 & pm=3 -> (sp'=5); // idlelp
[tick2] sp=6 & pm=3 -> (sp'=6); // stby
[tick2] sp=9 & pm=3 -> (sp'=9); // sleep
// goto_sleep
[tick2] sp=0 & pm=4 -> (sp'=8); // active
[tick2] sp=1 & pm=4 -> (sp'=8); // idle
[tick2] sp=3 & pm=4 -> (sp'=8); // idlelp
[tick2] sp=6 & pm=4 -> (sp'=8); // stby
[tick2] sp=9 & pm=4 -> (sp'=9); // sleep
endmodule
//-------------------------------------------------------------------------
// SQ
module SQ
q : [0..QMAX] init 0;
// serve if busy
[tick2] sr=0 & sp=0 -> (q'=max(q-1,0));
[tick2] sr=1 & sp=0 -> (q'=q);
// otherwise do nothing
[tick2] sr=0 & sp>0 -> (q'=q);
[tick2] sr=1 & sp>0 -> (q'=min(q+1,QMAX));
endmodule
//-------------------------------------------------------------------------
//rewards "time"
// [tick2] bat=1 : 1;
//endrewards
rewards "power"
[tick2] sp=0 & c=1 : 2.5;
[tick2] sp=1 & c=1 : 1.5;
[tick2] sp=2 & c=1 : 2.5;
[tick2] sp=3 & c=1 : 0.8;
[tick2] sp=4 & c=1 : 2.5;
[tick2] sp=5 & c=1 : 2.5;
[tick2] sp=6 & c=1 : 0.3;
[tick2] sp=7 & c=1 : 2.5;
[tick2] sp=8 & c=1 : 2.5;
[tick2] sp=9 & c=1 : 0.1;
[tick2] sp=10 & c=1 : 2.5;
endrewards
// is an instantaneous property but I suppose we can look at average size
// i.e. divide by the expected number of time steps
rewards "queue"
[tick2] c=1 : q;
endrewards
rewards "lost"
[tick2] sr=1 & sp>0 & q=2 : 1;
endrewards

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examples/multiobjective/mdp/dpm/dpm200_numerical.pctl
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multi(R{"power"}min=? [ C<=200 ], R{"queue"}<=170 [ C<=200 ])
// Note: The property file from http://www.prismmodelchecker.org/files/atva12mo/ does not provide a threshold for the second objective.
// We pick a threshold that intersects the pareto curve.

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examples/multiobjective/mdp/dpm/dpm200_pareto.pctl
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multi(R{"power"}min=? [ C<=200 ], R{"queue"}min=? [ C<=200 ])

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examples/multiobjective/mdp/dpm/dpm300.nm
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// power manager example
mdp
const int QMAX=2; // max queue size
// to model the pm making a choice and then a move being made we need
// two clock ticks for each transition
// first the pm decides tick1 and then the system moves tick2
module timer
c : [0..1];
[tick1] c=0 -> (c'=1);
[tick2] c=1 -> (c'=0);
endmodule
//-------------------------------------------------------------------------
// POWER MANAGER
module PM
pm : [0..4] init 4;
// 0 - go to active
// 1 - go to idle
// 2 - go to idlelp
// 3 - go to stby
// 4 - go to sleep
[tick1] true -> (pm'=0);
[tick1] true -> (pm'=1);
[tick1] true -> (pm'=2);
[tick1] true -> (pm'=3);
[tick1] true -> (pm'=4);
endmodule
//-------------------------------------------------------------------------
// SERVICE REQUESTER
module SR
sr : [0..1] init 0;
// 0 idle
// 1 1req
[tick2] sr=0 -> 0.898: (sr'=0) + 0.102: (sr'=1);
[tick2] sr=1 -> 0.454: (sr'=0) + 0.546: (sr'=1);
endmodule
//-------------------------------------------------------------------------
// SERVICE PROVIDER
module SP
sp : [0..10] init 9;
// 0 active
// 1 idle
// 2 active_idlelp
// 3 idlelp
// 4 idlelp_active
// 5 active_stby
// 6 stby
// 7 stby_active
// 8 active_sleep
// 9 sleep
// 10 sleep_active
// states where PM has no control (transient states)
[tick2] sp=2 -> 0.75 : (sp'=2) + 0.25 : (sp'=3); // active_idlelp
[tick2] sp=4 -> 0.25 : (sp'=0) + 0.75 : (sp'=4); // idlelp_active
[tick2] sp=5 -> 0.995 : (sp'=5) + 0.005 : (sp'=6); // active_stby
[tick2] sp=7 -> 0.005 : (sp'=0) + 0.995 : (sp'=7); // stby_active
[tick2] sp=8 -> 0.9983 : (sp'=8) + 0.0017 : (sp'=9); // active_sleep
[tick2] sp=10 -> 0.0017 : (sp'=0) + 0.9983 : (sp'=10); // sleep_active
// states where PM has control
// goto_active
[tick2] sp=0 & pm=0 -> (sp'=0); // active
[tick2] sp=1 & pm=0 -> (sp'=0); // idle
[tick2] sp=3 & pm=0 -> (sp'=4); // idlelp
[tick2] sp=6 & pm=0 -> (sp'=7); // stby
[tick2] sp=9 & pm=0 -> (sp'=10); // sleep
// goto_idle
[tick2] sp=0 & pm=1 -> (sp'=1); // active
[tick2] sp=1 & pm=1 -> (sp'=1); // idle
[tick2] sp=3 & pm=1 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=1 -> (sp'=6); // stby
[tick2] sp=9 & pm=1 -> (sp'=9); // sleep
// goto_idlelp
[tick2] sp=0 & pm=2 -> (sp'=2); // active
[tick2] sp=1 & pm=2 -> (sp'=2); // idle
[tick2] sp=3 & pm=2 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=2 -> (sp'=6); // stby
[tick2] sp=9 & pm=2 -> (sp'=9); // sleep
// goto_stby
[tick2] sp=0 & pm=3 -> (sp'=5); // active
[tick2] sp=1 & pm=3 -> (sp'=5); // idle
[tick2] sp=3 & pm=3 -> (sp'=5); // idlelp
[tick2] sp=6 & pm=3 -> (sp'=6); // stby
[tick2] sp=9 & pm=3 -> (sp'=9); // sleep
// goto_sleep
[tick2] sp=0 & pm=4 -> (sp'=8); // active
[tick2] sp=1 & pm=4 -> (sp'=8); // idle
[tick2] sp=3 & pm=4 -> (sp'=8); // idlelp
[tick2] sp=6 & pm=4 -> (sp'=8); // stby
[tick2] sp=9 & pm=4 -> (sp'=9); // sleep
endmodule
//-------------------------------------------------------------------------
// SQ
module SQ
q : [0..QMAX] init 0;
// serve if busy
[tick2] sr=0 & sp=0 -> (q'=max(q-1,0));
[tick2] sr=1 & sp=0 -> (q'=q);
// otherwise do nothing
[tick2] sr=0 & sp>0 -> (q'=q);
[tick2] sr=1 & sp>0 -> (q'=min(q+1,QMAX));
endmodule
//-------------------------------------------------------------------------
//rewards "time"
// [tick2] bat=1 : 1;
//endrewards
rewards "power"
[tick2] sp=0 & c=1 : 2.5;
[tick2] sp=1 & c=1 : 1.5;
[tick2] sp=2 & c=1 : 2.5;
[tick2] sp=3 & c=1 : 0.8;
[tick2] sp=4 & c=1 : 2.5;
[tick2] sp=5 & c=1 : 2.5;
[tick2] sp=6 & c=1 : 0.3;
[tick2] sp=7 & c=1 : 2.5;
[tick2] sp=8 & c=1 : 2.5;
[tick2] sp=9 & c=1 : 0.1;
[tick2] sp=10 & c=1 : 2.5;
endrewards
// is an instantaneous property but I suppose we can look at average size
// i.e. divide by the expected number of time steps
rewards "queue"
[tick2] c=1 : q;
endrewards
rewards "lost"
[tick2] sr=1 & sp>0 & q=2 : 1;
endrewards

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examples/multiobjective/mdp/dpm/dpm300_numerical.pctl
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multi(R{"power"}min=? [ C<=300 ], R{"queue"}<=270 [ C<=300 ])
// Note: The property file from http://www.prismmodelchecker.org/files/atva12mo/ does not provide a threshold for the second objective.
// We pick a threshold that intersects the pareto curve.

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examples/multiobjective/mdp/dpm/dpm300_pareto.pctl
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multi(R{"power"}min=? [ C<=300 ], R{"queue"}min=? [ C<=300 ])

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examples/multiobjective/mdp/dpm/origFiles/power-timed.nm
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// power manager example
mdp
const int QMAX; // max queue size
// to model the pm making a choice and then a move being made we need
// two clock ticks for each transition
// first the pm decides tick1 and then the system moves tick2
module timer
c : [0..1];
[tick1] c=0 -> (c'=1);
[tick2] c=1 -> (c'=0);
endmodule
//-------------------------------------------------------------------------
// POWER MANAGER
module PM
pm : [0..4] init 4;
// 0 - go to active
// 1 - go to idle
// 2 - go to idlelp
// 3 - go to stby
// 4 - go to sleep
[tick1] true -> (pm'=0);
[tick1] true -> (pm'=1);
[tick1] true -> (pm'=2);
[tick1] true -> (pm'=3);
[tick1] true -> (pm'=4);
endmodule
//-------------------------------------------------------------------------
// SERVICE REQUESTER
module SR
sr : [0..1] init 0;
// 0 idle
// 1 1req
[tick2] sr=0 -> 0.898: (sr'=0) + 0.102: (sr'=1);
[tick2] sr=1 -> 0.454: (sr'=0) + 0.546: (sr'=1);
endmodule
//-------------------------------------------------------------------------
// SERVICE PROVIDER
module SP
sp : [0..10] init 9;
// 0 active
// 1 idle
// 2 active_idlelp
// 3 idlelp
// 4 idlelp_active
// 5 active_stby
// 6 stby
// 7 stby_active
// 8 active_sleep
// 9 sleep
// 10 sleep_active
// states where PM has no control (transient states)
[tick2] sp=2 -> 0.75 : (sp'=2) + 0.25 : (sp'=3); // active_idlelp
[tick2] sp=4 -> 0.25 : (sp'=0) + 0.75 : (sp'=4); // idlelp_active
[tick2] sp=5 -> 0.995 : (sp'=5) + 0.005 : (sp'=6); // active_stby
[tick2] sp=7 -> 0.005 : (sp'=0) + 0.995 : (sp'=7); // stby_active
[tick2] sp=8 -> 0.9983 : (sp'=8) + 0.0017 : (sp'=9); // active_sleep
[tick2] sp=10 -> 0.0017 : (sp'=0) + 0.9983 : (sp'=10); // sleep_active
// states where PM has control
// goto_active
[tick2] sp=0 & pm=0 -> (sp'=0); // active
[tick2] sp=1 & pm=0 -> (sp'=0); // idle
[tick2] sp=3 & pm=0 -> (sp'=4); // idlelp
[tick2] sp=6 & pm=0 -> (sp'=7); // stby
[tick2] sp=9 & pm=0 -> (sp'=10); // sleep
// goto_idle
[tick2] sp=0 & pm=1 -> (sp'=1); // active
[tick2] sp=1 & pm=1 -> (sp'=1); // idle
[tick2] sp=3 & pm=1 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=1 -> (sp'=6); // stby
[tick2] sp=9 & pm=1 -> (sp'=9); // sleep
// goto_idlelp
[tick2] sp=0 & pm=2 -> (sp'=2); // active
[tick2] sp=1 & pm=2 -> (sp'=2); // idle
[tick2] sp=3 & pm=2 -> (sp'=3); // idlelp
[tick2] sp=6 & pm=2 -> (sp'=6); // stby
[tick2] sp=9 & pm=2 -> (sp'=9); // sleep
// goto_stby
[tick2] sp=0 & pm=3 -> (sp'=5); // active
[tick2] sp=1 & pm=3 -> (sp'=5); // idle
[tick2] sp=3 & pm=3 -> (sp'=5); // idlelp
[tick2] sp=6 & pm=3 -> (sp'=6); // stby
[tick2] sp=9 & pm=3 -> (sp'=9); // sleep
// goto_sleep
[tick2] sp=0 & pm=4 -> (sp'=8); // active
[tick2] sp=1 & pm=4 -> (sp'=8); // idle
[tick2] sp=3 & pm=4 -> (sp'=8); // idlelp
[tick2] sp=6 & pm=4 -> (sp'=8); // stby
[tick2] sp=9 & pm=4 -> (sp'=9); // sleep
endmodule
//-------------------------------------------------------------------------
// SQ
module SQ
q : [0..QMAX] init 0;
// serve if busy
[tick2] sr=0 & sp=0 -> (q'=max(q-1,0));
[tick2] sr=1 & sp=0 -> (q'=q);
// otherwise do nothing
[tick2] sr=0 & sp>0 -> (q'=q);
[tick2] sr=1 & sp>0 -> (q'=min(q+1,QMAX));
endmodule
//-------------------------------------------------------------------------
//rewards "time"
// [tick2] bat=1 : 1;
//endrewards
rewards "power"
[tick2] sp=0 & c=1 : 2.5;
[tick2] sp=1 & c=1 : 1.5;
[tick2] sp=2 & c=1 : 2.5;
[tick2] sp=3 & c=1 : 0.8;
[tick2] sp=4 & c=1 : 2.5;
[tick2] sp=5 & c=1 : 2.5;
[tick2] sp=6 & c=1 : 0.3;
[tick2] sp=7 & c=1 : 2.5;
[tick2] sp=8 & c=1 : 2.5;
[tick2] sp=9 & c=1 : 0.1;
[tick2] sp=10 & c=1 : 2.5;
endrewards
// is an instantaneous property but I suppose we can look at average size
// i.e. divide by the expected number of time steps
rewards "queue"
[tick2] c=1 : q;
endrewards
rewards "lost"
[tick2] sr=1 & sp>0 & q=2 : 1;
endrewards

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examples/multiobjective/mdp/dpm/origFiles/power-timed.pctl
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// Average queue size
const double Q;
// Time bound
const int k;
// Minimum energy usage over k time-steps, such that average queue size remains below Q
"num_energy": multi(R{"power"}min=? [ C<=k ], R{"queue"}<=Q*k [ C<=k ])
// Pareto query: minimum energy usage vs minimum average queue size
"pareto": multi(R{"power"}min=? [ C<=k ], R{"queue"}min=? [ C<=k ])

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examples/multiobjective/mdp/scheduler/origFiles/scheduler.pctl
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// Minimise expected completion time given a bound on expected energy usage
"num_time": multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ])
// Minimise expected energy usage given a bound on expected completion time
"num_energy": multi( R{"energy"}min=?[ C ], R{"time"}<=1000[ C ])
// Pareto query for assume-guarantee check
"pareto": multi(R{"energy"}min=?[ C ], R{"time"}min=? [ C ])

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examples/multiobjective/mdp/scheduler/origFiles/scheduler_prob2_K.nm
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mdp
label "tasks_complete" = (task6=3);
const int K;
module scheduler
task1 : [0..3];
task2 : [0..3];
task3 : [0..3];
task4 : [0..3];
task5 : [0..3];
task6 : [0..3];
[p1_add] task1=0 -> (task1'=1);
[p2_add] task1=0 -> (task1'=2);
[p1_mult] task2=0 -> (task2'=1);
[p2_mult] task2=0 -> (task2'=2);
[p1_mult] task3=0&task1=3 -> (task3'=1);
[p2_mult] task3=0&task1=3 -> (task3'=2);
[p1_add] task4=0&task1=3&task2=3 -> (task4'=1);
[p2_add] task4=0&task1=3&task2=3 -> (task4'=2);
[p1_mult] task5=0&task3=3 -> (task5'=1);
[p2_mult] task5=0&task3=3 -> (task5'=2);
[p1_add] task6=0&task4=3&task5=3 -> (task6'=1);
[p2_add] task6=0&task4=3&task5=3 -> (task6'=2);
[p1_done] task1=1 -> (task1'=3);
[p1_done] task2=1 -> (task2'=3);
[p1_done] task3=1 -> (task3'=3);
[p1_done] task4=1 -> (task4'=3);
[p1_done] task5=1 -> (task5'=3);
[p1_done] task6=1 -> (task6'=3);
[p2_done] task1=2 -> (task1'=3);
[p2_done] task2=2 -> (task2'=3);
[p2_done] task3=2 -> (task3'=3);
[p2_done] task4=2 -> (task4'=3);
[p2_done] task5=2 -> (task5'=3);
[p2_done] task6=2 -> (task6'=3);
[time] true -> 1.0 : true;
endmodule
module P1
p1 : [0..3];
c1 : [0..2];
x1 : [0..4*K+1];
[p1_add] (p1=0) -> (p1'=1) & (x1'=0);
[] (p1=1)&(x1=1*K)&(c1=0) -> 1/3 : (p1'=3) & (x1'=0) & (c1'=0) + 2/3 : (c1'=1) & (x1'=0);
[] (p1=1)&(x1=1*K)&(c1=1) -> 1/2 : (p1'=3) & (x1'=0) & (c1'=0) + 1/2 : (c1'=2) & (x1'=0);
[p1_done] (p1=1)&(x1=1*K)&(c1=2) -> (p1'=0) & (x1'=0) & (c1'=0);
[p1_mult] (p1=0) -> (p1'=2) & (x1'=0);
[] (p1=2)&(x1=2*K)&(c1=0) -> 1/3 : (p1'=3) & (x1'=0) & (c1'=0) + 2/3 : (c1'=1) & (x1'=0);
[] (p1=2)&(x1=1*K)&(c1=1) -> 1/2 : (p1'=3) & (x1'=0) & (c1'=0) + 1/2 : (c1'=2) & (x1'=0);
[p1_done] (p1=2)&(x1=1*K)&(c1=2) -> (p1'=0) & (x1'=0) & (c1'=0);
[p1_done] (p1=3) -> (p1'=0);
[time] (p1=1=>x1+1<=1*K)&((p1=2&c1=0)=>x1+1<=2*K)&((p1=2&c1>0)=>x1+1<=1*K)&(p1=3=>x1+1<=0) -> 1.0 : (x1'=min(x1+1,4*K+1));
endmodule
module P2
p2 : [0..3];
c2 : [0..2];
x2 : [0..6*K+1];
[p2_add] (p2=0) -> (p2'=1) & (x2'=0);
[] (p2=1)&(x2=4*K)&(c2=0) -> 1/3 : (p2'=3) & (x2'=0) & (c2'=0) + 2/3 : (c2'=1) & (x2'=0);
[] (p2=1)&(x2=1)&(c2=1) -> 1/2 : (p2'=3) & (x2'=0) & (c2'=0) + 1/2 : (c2'=2) & (x2'=0);
[p2_done] (p2=1)&(x2=1)&(c2=2) -> (p2'=0) & (x2'=0) & (c2'=0);
[p2_mult] (p2=0) -> (p2'=2) & (x2'=0);
[] (p2=2)&(x2=6*K)&(c2=0) -> 1/3 : (p2'=3) & (x2'=0) & (c2'=0) + 2/3 : (c2'=1) & (x2'=0);
[] (p2=2)&(x2=1)&(c2=1) -> 1/2 : (p2'=3) & (x2'=0) & (c2'=0) + 1/2 : (c2'=2) & (x2'=0);
[p2_done] (p2=2)&(x2=1)&(c2=2) -> (p2'=0) & (x2'=0) & (c2'=0);
[p2_done] (p2=3) -> (p2'=0);
[time] ((p2=1&c2=0)=>x2+1<=4*K)&((p2=1&c2>0)=>x2+1<=1)&((p2=2&c2=0)=>x2+1<=6*K)&((p2=2&c2>0)=>x2+1<=1)&(p2=3=>x2+1<=0) -> 1.0 : (x2'=min(x2+1,6*K+1));
endmodule
rewards "time"
[time] true : 1/K;
endrewards
rewards "energy"
[time] p1=0 : 10/(1000*K);
[time] p1>0 : 90/(1000*K);
[time] p2=0 : 20/(1000*K);
[time] p2>0 : 30/(1000*K);
endrewards

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examples/multiobjective/mdp/scheduler/scheduler05.nm
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mdp
label "tasks_complete" = (task6=3);
const int K=5;
module scheduler
task1 : [0..3];
task2 : [0..3];
task3 : [0..3];
task4 : [0..3];
task5 : [0..3];
task6 : [0..3];
[p1_add] task1=0 -> (task1'=1);
[p2_add] task1=0 -> (task1'=2);
[p1_mult] task2=0 -> (task2'=1);
[p2_mult] task2=0 -> (task2'=2);
[p1_mult] task3=0&task1=3 -> (task3'=1);
[p2_mult] task3=0&task1=3 -> (task3'=2);
[p1_add] task4=0&task1=3&task2=3 -> (task4'=1);
[p2_add] task4=0&task1=3&task2=3 -> (task4'=2);
[p1_mult] task5=0&task3=3 -> (task5'=1);
[p2_mult] task5=0&task3=3 -> (task5'=2);
[p1_add] task6=0&task4=3&task5=3 -> (task6'=1);
[p2_add] task6=0&task4=3&task5=3 -> (task6'=2);
[p1_done] task1=1 -> (task1'=3);
[p1_done] task2=1 -> (task2'=3);
[p1_done] task3=1 -> (task3'=3);
[p1_done] task4=1 -> (task4'=3);
[p1_done] task5=1 -> (task5'=3);
[p1_done] task6=1 -> (task6'=3);
[p2_done] task1=2 -> (task1'=3);
[p2_done] task2=2 -> (task2'=3);
[p2_done] task3=2 -> (task3'=3);
[p2_done] task4=2 -> (task4'=3);
[p2_done] task5=2 -> (task5'=3);
[p2_done] task6=2 -> (task6'=3);
[time] true -> 1.0 : true;
endmodule
module P1
p1 : [0..3];
c1 : [0..2];
x1 : [0..4*K+1];
[p1_add] (p1=0) -> (p1'=1) & (x1'=0);
[] (p1=1)&(x1=1*K)&(c1=0) -> 1/3 : (p1'=3) & (x1'=0) & (c1'=0) + 2/3 : (c1'=1) & (x1'=0);
[] (p1=1)&(x1=1*K)&(c1=1) -> 1/2 : (p1'=3) & (x1'=0) & (c1'=0) + 1/2 : (c1'=2) & (x1'=0);
[p1_done] (p1=1)&(x1=1*K)&(c1=2) -> (p1'=0) & (x1'=0) & (c1'=0);
[p1_mult] (p1=0) -> (p1'=2) & (x1'=0);
[] (p1=2)&(x1=2*K)&(c1=0) -> 1/3 : (p1'=3) & (x1'=0) & (c1'=0) + 2/3 : (c1'=1) & (x1'=0);
[] (p1=2)&(x1=1*K)&(c1=1) -> 1/2 : (p1'=3) & (x1'=0) & (c1'=0) + 1/2 : (c1'=2) & (x1'=0);
[p1_done] (p1=2)&(x1=1*K)&(c1=2) -> (p1'=0) & (x1'=0) & (c1'=0);
[p1_done] (p1=3) -> (p1'=0);
[time] (p1=1=>x1+1<=1*K)&((p1=2&c1=0)=>x1+1<=2*K)&((p1=2&c1>0)=>x1+1<=1*K)&(p1=3=>x1+1<=0) -> 1.0 : (x1'=min(x1+1,4*K+1));
endmodule
module P2
p2 : [0..3];
c2 : [0..2];
x2 : [0..6*K+1];
[p2_add] (p2=0) -> (p2'=1) & (x2'=0);
[] (p2=1)&(x2=4*K)&(c2=0) -> 1/3 : (p2'=3) & (x2'=0) & (c2'=0) + 2/3 : (c2'=1) & (x2'=0);
[] (p2=1)&(x2=1)&(c2=1) -> 1/2 : (p2'=3) & (x2'=0) & (c2'=0) + 1/2 : (c2'=2) & (x2'=0);
[p2_done] (p2=1)&(x2=1)&(c2=2) -> (p2'=0) & (x2'=0) & (c2'=0);
[p2_mult] (p2=0) -> (p2'=2) & (x2'=0);
[] (p2=2)&(x2=6*K)&(c2=0) -> 1/3 : (p2'=3) & (x2'=0) & (c2'=0) + 2/3 : (c2'=1) & (x2'=0);
[] (p2=2)&(x2=1)&(c2=1) -> 1/2 : (p2'=3) & (x2'=0) & (c2'=0) + 1/2 : (c2'=2) & (x2'=0);
[p2_done] (p2=2)&(x2=1)&(c2=2) -> (p2'=0) & (x2'=0) & (c2'=0);
[p2_done] (p2=3) -> (p2'=0);
[time] ((p2=1&c2=0)=>x2+1<=4*K)&((p2=1&c2>0)=>x2+1<=1)&((p2=2&c2=0)=>x2+1<=6*K)&((p2=2&c2>0)=>x2+1<=1)&(p2=3=>x2+1<=0) -> 1.0 : (x2'=min(x2+1,6*K+1));
endmodule
rewards "time"
[time] true : 1/K;
endrewards
rewards "energy"
[time] p1=0 : 10/(1000*K);
[time] p1>0 : 90/(1000*K);
[time] p2=0 : 20/(1000*K);
[time] p2>0 : 30/(1000*K);
endrewards

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examples/multiobjective/mdp/scheduler/scheduler05_numerical.pctl
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multi(R{"time"}min=?[ F "tasks_complete" ], R{"energy"}<=1.45 [ F "tasks_complete" ])
// Original query:
//multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ])
// Note that the min values are actually infinity and prism (currently) gives wrong results for this, e.g., R{"time"}min=?[ C<=2000 ] gives a larger value than multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ]) .

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examples/multiobjective/mdp/scheduler/scheduler05_pareto.pctl
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multi(R{"time"}min=?[ F "tasks_complete" ], R{"energy"}min=? [ F "tasks_complete" ])
// Original query:
//multi(R{"energy"}min=?[ C ], R{"time"}min=? [ C ])
// Note that the min values are actually infinity and prism (currently) gives wrong results for this, e.g., R{"time"}min=?[ C<=2000 ] gives a larger value than multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ]) .

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examples/multiobjective/mdp/scheduler/scheduler25.nm
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mdp
label "tasks_complete" = (task6=3);
const int K=25;
module scheduler
task1 : [0..3];
task2 : [0..3];
task3 : [0..3];
task4 : [0..3];
task5 : [0..3];
task6 : [0..3];
[p1_add] task1=0 -> (task1'=1);
[p2_add] task1=0 -> (task1'=2);
[p1_mult] task2=0 -> (task2'=1);
[p2_mult] task2=0 -> (task2'=2);
[p1_mult] task3=0&task1=3 -> (task3'=1);
[p2_mult] task3=0&task1=3 -> (task3'=2);
[p1_add] task4=0&task1=3&task2=3 -> (task4'=1);
[p2_add] task4=0&task1=3&task2=3 -> (task4'=2);
[p1_mult] task5=0&task3=3 -> (task5'=1);
[p2_mult] task5=0&task3=3 -> (task5'=2);
[p1_add] task6=0&task4=3&task5=3 -> (task6'=1);
[p2_add] task6=0&task4=3&task5=3 -> (task6'=2);
[p1_done] task1=1 -> (task1'=3);
[p1_done] task2=1 -> (task2'=3);
[p1_done] task3=1 -> (task3'=3);
[p1_done] task4=1 -> (task4'=3);
[p1_done] task5=1 -> (task5'=3);
[p1_done] task6=1 -> (task6'=3);
[p2_done] task1=2 -> (task1'=3);
[p2_done] task2=2 -> (task2'=3);
[p2_done] task3=2 -> (task3'=3);
[p2_done] task4=2 -> (task4'=3);
[p2_done] task5=2 -> (task5'=3);
[p2_done] task6=2 -> (task6'=3);
[time] true -> 1.0 : true;
endmodule
module P1
p1 : [0..3];
c1 : [0..2];
x1 : [0..4*K+1];
[p1_add] (p1=0) -> (p1'=1) & (x1'=0);
[] (p1=1)&(x1=1*K)&(c1=0) -> 1/3 : (p1'=3) & (x1'=0) & (c1'=0) + 2/3 : (c1'=1) & (x1'=0);
[] (p1=1)&(x1=1*K)&(c1=1) -> 1/2 : (p1'=3) & (x1'=0) & (c1'=0) + 1/2 : (c1'=2) & (x1'=0);
[p1_done] (p1=1)&(x1=1*K)&(c1=2) -> (p1'=0) & (x1'=0) & (c1'=0);
[p1_mult] (p1=0) -> (p1'=2) & (x1'=0);
[] (p1=2)&(x1=2*K)&(c1=0) -> 1/3 : (p1'=3) & (x1'=0) & (c1'=0) + 2/3 : (c1'=1) & (x1'=0);
[] (p1=2)&(x1=1*K)&(c1=1) -> 1/2 : (p1'=3) & (x1'=0) & (c1'=0) + 1/2 : (c1'=2) & (x1'=0);
[p1_done] (p1=2)&(x1=1*K)&(c1=2) -> (p1'=0) & (x1'=0) & (c1'=0);
[p1_done] (p1=3) -> (p1'=0);
[time] (p1=1=>x1+1<=1*K)&((p1=2&c1=0)=>x1+1<=2*K)&((p1=2&c1>0)=>x1+1<=1*K)&(p1=3=>x1+1<=0) -> 1.0 : (x1'=min(x1+1,4*K+1));
endmodule
module P2
p2 : [0..3];
c2 : [0..2];
x2 : [0..6*K+1];
[p2_add] (p2=0) -> (p2'=1) & (x2'=0);
[] (p2=1)&(x2=4*K)&(c2=0) -> 1/3 : (p2'=3) & (x2'=0) & (c2'=0) + 2/3 : (c2'=1) & (x2'=0);
[] (p2=1)&(x2=1)&(c2=1) -> 1/2 : (p2'=3) & (x2'=0) & (c2'=0) + 1/2 : (c2'=2) & (x2'=0);
[p2_done] (p2=1)&(x2=1)&(c2=2) -> (p2'=0) & (x2'=0) & (c2'=0);
[p2_mult] (p2=0) -> (p2'=2) & (x2'=0);
[] (p2=2)&(x2=6*K)&(c2=0) -> 1/3 : (p2'=3) & (x2'=0) & (c2'=0) + 2/3 : (c2'=1) & (x2'=0);
[] (p2=2)&(x2=1)&(c2=1) -> 1/2 : (p2'=3) & (x2'=0) & (c2'=0) + 1/2 : (c2'=2) & (x2'=0);
[p2_done] (p2=2)&(x2=1)&(c2=2) -> (p2'=0) & (x2'=0) & (c2'=0);
[p2_done] (p2=3) -> (p2'=0);
[time] ((p2=1&c2=0)=>x2+1<=4*K)&((p2=1&c2>0)=>x2+1<=1)&((p2=2&c2=0)=>x2+1<=6*K)&((p2=2&c2>0)=>x2+1<=1)&(p2=3=>x2+1<=0) -> 1.0 : (x2'=min(x2+1,6*K+1));
endmodule
rewards "time"
[time] true : 1/K;
endrewards
rewards "energy"
[time] p1=0 : 10/(1000*K);
[time] p1>0 : 90/(1000*K);
[time] p2=0 : 20/(1000*K);
[time] p2>0 : 30/(1000*K);
endrewards

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examples/multiobjective/mdp/scheduler/scheduler25_numerical.pctl
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multi(R{"time"}min=?[ F "tasks_complete" ], R{"energy"}<=1.45 [ F "tasks_complete" ])
// Original query:
// multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ])
// Note that the min values are actually infinity and prism (currently) gives wrong results for this, e.g., R{"time"}min=?[ C<=2000 ] gives a larger value than multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ]) .

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examples/multiobjective/mdp/scheduler/scheduler25_pareto.pctl
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multi(R{"time"}min=?[ F "tasks_complete" ], R{"energy"}min=? [ F "tasks_complete" ])
// Original query:
// multi(R{"energy"}min=?[ C ], R{"time"}min=? [ C ])
// Note that the min values are actually infinity and prism (currently) gives wrong results for this, e.g., R{"time"}min=?[ C<=2000 ] gives a larger value than multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ]) .

95
examples/multiobjective/mdp/scheduler/scheduler50.nm
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mdp
label "tasks_complete" = (task6=3);
const int K=50;
module scheduler
task1 : [0..3];
task2 : [0..3];
task3 : [0..3];
task4 : [0..3];
task5 : [0..3];
task6 : [0..3];
[p1_add] task1=0 -> (task1'=1);
[p2_add] task1=0 -> (task1'=2);
[p1_mult] task2=0 -> (task2'=1);
[p2_mult] task2=0 -> (task2'=2);
[p1_mult] task3=0&task1=3 -> (task3'=1);
[p2_mult] task3=0&task1=3 -> (task3'=2);
[p1_add] task4=0&task1=3&task2=3 -> (task4'=1);
[p2_add] task4=0&task1=3&task2=3 -> (task4'=2);
[p1_mult] task5=0&task3=3 -> (task5'=1);
[p2_mult] task5=0&task3=3 -> (task5'=2);
[p1_add] task6=0&task4=3&task5=3 -> (task6'=1);
[p2_add] task6=0&task4=3&task5=3 -> (task6'=2);
[p1_done] task1=1 -> (task1'=3);
[p1_done] task2=1 -> (task2'=3);
[p1_done] task3=1 -> (task3'=3);
[p1_done] task4=1 -> (task4'=3);
[p1_done] task5=1 -> (task5'=3);
[p1_done] task6=1 -> (task6'=3);
[p2_done] task1=2 -> (task1'=3);
[p2_done] task2=2 -> (task2'=3);
[p2_done] task3=2 -> (task3'=3);
[p2_done] task4=2 -> (task4'=3);
[p2_done] task5=2 -> (task5'=3);
[p2_done] task6=2 -> (task6'=3);
[time] true -> 1.0 : true;
endmodule
module P1
p1 : [0..3];
c1 : [0..2];
x1 : [0..4*K+1];
[p1_add] (p1=0) -> (p1'=1) & (x1'=0);
[] (p1=1)&(x1=1*K)&(c1=0) -> 1/3 : (p1'=3) & (x1'=0) & (c1'=0) + 2/3 : (c1'=1) & (x1'=0);
[] (p1=1)&(x1=1*K)&(c1=1) -> 1/2 : (p1'=3) & (x1'=0) & (c1'=0) + 1/2 : (c1'=2) & (x1'=0);
[p1_done] (p1=1)&(x1=1*K)&(c1=2) -> (p1'=0) & (x1'=0) & (c1'=0);
[p1_mult] (p1=0) -> (p1'=2) & (x1'=0);
[] (p1=2)&(x1=2*K)&(c1=0) -> 1/3 : (p1'=3) & (x1'=0) & (c1'=0) + 2/3 : (c1'=1) & (x1'=0);
[] (p1=2)&(x1=1*K)&(c1=1) -> 1/2 : (p1'=3) & (x1'=0) & (c1'=0) + 1/2 : (c1'=2) & (x1'=0);
[p1_done] (p1=2)&(x1=1*K)&(c1=2) -> (p1'=0) & (x1'=0) & (c1'=0);
[p1_done] (p1=3) -> (p1'=0);
[time] (p1=1=>x1+1<=1*K)&((p1=2&c1=0)=>x1+1<=2*K)&((p1=2&c1>0)=>x1+1<=1*K)&(p1=3=>x1+1<=0) -> 1.0 : (x1'=min(x1+1,4*K+1));
endmodule
module P2
p2 : [0..3];
c2 : [0..2];
x2 : [0..6*K+1];
[p2_add] (p2=0) -> (p2'=1) & (x2'=0);
[] (p2=1)&(x2=4*K)&(c2=0) -> 1/3 : (p2'=3) & (x2'=0) & (c2'=0) + 2/3 : (c2'=1) & (x2'=0);
[] (p2=1)&(x2=1)&(c2=1) -> 1/2 : (p2'=3) & (x2'=0) & (c2'=0) + 1/2 : (c2'=2) & (x2'=0);
[p2_done] (p2=1)&(x2=1)&(c2=2) -> (p2'=0) & (x2'=0) & (c2'=0);
[p2_mult] (p2=0) -> (p2'=2) & (x2'=0);
[] (p2=2)&(x2=6*K)&(c2=0) -> 1/3 : (p2'=3) & (x2'=0) & (c2'=0) + 2/3 : (c2'=1) & (x2'=0);
[] (p2=2)&(x2=1)&(c2=1) -> 1/2 : (p2'=3) & (x2'=0) & (c2'=0) + 1/2 : (c2'=2) & (x2'=0);
[p2_done] (p2=2)&(x2=1)&(c2=2) -> (p2'=0) & (x2'=0) & (c2'=0);
[p2_done] (p2=3) -> (p2'=0);
[time] ((p2=1&c2=0)=>x2+1<=4*K)&((p2=1&c2>0)=>x2+1<=1)&((p2=2&c2=0)=>x2+1<=6*K)&((p2=2&c2>0)=>x2+1<=1)&(p2=3=>x2+1<=0) -> 1.0 : (x2'=min(x2+1,6*K+1));
endmodule
rewards "time"
[time] true : 1/K;
endrewards
rewards "energy"
[time] p1=0 : 10/(1000*K);
[time] p1>0 : 90/(1000*K);
[time] p2=0 : 20/(1000*K);
[time] p2>0 : 30/(1000*K);
endrewards

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examples/multiobjective/mdp/scheduler/scheduler50_numerical.pctl
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multi(R{"time"}min=?[ F "tasks_complete" ], R{"energy"}<=1.45 [ F "tasks_complete" ])
// Original query:
// multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ])
// Note that the min values are actually infinity and prism (currently) gives wrong results for this, e.g., R{"time"}min=?[ C<=2000 ] gives a larger value than multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ]) .

4
examples/multiobjective/mdp/scheduler/scheduler50_pareto.pctl
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multi(R{"time"}min=?[ F "tasks_complete" ], R{"energy"}min=? [ F "tasks_complete" ])
// Original query:
// multi(R{"energy"}min=?[ C ], R{"time"}min=? [ C ])
// Note that the min values are actually infinity and prism (currently) gives wrong results for this, e.g., R{"time"}min=?[ C<=2000 ] gives a larger value than multi(R{"time"}min=?[ C ], R{"energy"}<=1.45 [ C ]) .

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examples/multiobjective/mdp/simple/simple.nm
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mdp
module simple
// local state
s : [0..2] init 0;
[A] s=0 -> 0.2 : (s'=1) + 0.8 : (s'=0);
[B] s=0 -> 1 : (s'=2);
[C] s=0 -> 1 : (s'=0);
[] s>0 -> 1 : (s'=s);
endmodule
rewards "actA"
[A] true : 1;
endrewards
rewards "actB"
[B] true : 2;
endrewards
label "a" = s=1;
label "b" = s=2;

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examples/multiobjective/mdp/simple/simple.pctl
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multi(P<0.4 [ F "a"], P<0.3 [ F "b"] )
//multi(Pmin=? [ F<=10 "a"], R<0.3 [ F "b" | "a"] )

231
examples/multiobjective/mdp/team/origFiles/MDP_a2_r3_t2_full_exp.nm
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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 2;
// sensor resources
const int resource1=1;
const int resource2=2;
// network configuration
const int e12=1;
const int e21=e12;
module controller // schedules the algorithm
// algorithm status
status : [0..5];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/2 : (turn1'=1) & (turn2'=2) & (status'=1)
+ 1/2 : (turn1'=2) & (turn2'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[] status=4 -> (status'=5);
[] status=5 -> true;
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1;
formula team_size_t2 = m1_t2+m2_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 > 0;
formula can_join_t2 = e12*m2_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))) / (e12);
// labels and formulae for property specification
formula finished = (status=4);
label "end" = (status=5);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)));
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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examples/multiobjective/mdp/team/origFiles/MDP_a3_r3_t2_full_exp.nm
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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 3;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
// network configuration
const int e12=1;
const int e13=1;
const int e21=e12;
const int e23=1;
const int e31=e13;
const int e32=e23;
module controller // schedules the algorithm
// algorithm status
status : [0..6];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/6 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (status'=1)
+ 1/6 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (status'=1)
+ 1/6 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (status'=1)
+ 1/6 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (status'=1)
+ 1/6 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (status'=1)
+ 1/6 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[] status=5 -> (status'=6);
[] status=6 -> true;
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))) / (e12+e13);
// labels and formulae for property specification
formula finished = (status=5);
label "end" = (status=6);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)));
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 4;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
const int resource4=1;
// network configuration
const int e12=1;
const int e13=1;
const int e14=1;
const int e21=e12;
const int e23=1;
const int e24=1;
const int e31=e13;
const int e32=e23;
const int e34=1;
const int e41=e14;
const int e42=e24;
const int e43=e34;
module controller // schedules the algorithm
// algorithm status
status : [0..7];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
turn4 : [0..n_sensors];
turn5 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/24 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
[str4] status=2 & turn1=4 -> (status'=2);
[fin4] status=2 & turn1=4 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
[str4] status=3 & turn2=4 -> (status'=3);
[fin4] status=3 & turn2=4 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[str4] status=4 & turn3=4 -> (status'=4);
[fin4] status=4 & turn3=4 -> (status'=5);
// 4th round
[str1] status=5 & turn4=1 -> (status'=5);
[fin1] status=5 & turn4=1 -> (status'=6);
[str2] status=5 & turn4=2 -> (status'=5);
[fin2] status=5 & turn4=2 -> (status'=6);
[str3] status=5 & turn4=3 -> (status'=5);
[fin3] status=5 & turn4=3 -> (status'=6);
[str4] status=5 & turn4=4 -> (status'=5);
[fin4] status=5 & turn4=4 -> (status'=6);
[] status=6 -> (status'=7);
[] status=7 -> (status'=7);
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
module sensor4 = sensor1
[
state1=state4,
str1=str4,
fin1=fin4,
m1_t1=m4_t1,
m1_t2=m4_t2,
m4_t1=m1_t1,
m4_t2=m1_t2,
resource1=resource4,
resource4=resource1,
e12=e42,
e13=e43,
e14=e41,
e15=e45,
e41=e14,
e42=e12,
e43=e13,
e45=e15
]
endmodule
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1+m4_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2+m4_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 + e14*m4_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 + e14*m4_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3) | (m4_t1=1 & resource1=resource4);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3) | (m4_t2=1 & resource1=resource4);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))+e14*(1-((m4_t1+m4_t2)=0?0:1))) / (e12+e13+e14);
// labels and formulae for property specification
formula finished = (status=6);
label "end" = (status=7);
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
formula agent4_joins_successful_team = (task1_completed & m4_t1=1) | (task2_completed & m4_t2=1);
formula agent4_joins_successful_team_of_1 = (task1_completed & m4_t1=1 & team_size_t1=1) | (task2_completed & m4_t2=1 & team_size_t2=1);
formula agent4_joins_successful_team_of_2 = (task1_completed & m4_t1=1 & team_size_t1=2) | (task2_completed & m4_t2=1 & team_size_t2=2);
formula agent4_joins_successful_team_of_3 = (task1_completed & m4_t1=1 & team_size_t1=3) | (task2_completed & m4_t2=1 & team_size_t2=3);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)|(m4_t1=1&resource4=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)|(m4_t1=1&resource4=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)|(m4_t1=1&resource4=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)|(m4_t2=1&resource4=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)|(m4_t2=1&resource4=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)|(m4_t2=1&resource4=3)));
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
[] agent4_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 5;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
const int resource4=1;
const int resource5=2;
// network configuration
const int e12=1;
const int e13=1;
const int e14=1;
const int e15=1;
const int e21=e12;
const int e23=1;
const int e24=1;
const int e25=1;
const int e31=e13;
const int e32=e23;
const int e34=1;
const int e35=1;
const int e41=e14;
const int e42=e24;
const int e43=e34;
const int e45=1;
const int e51=e15;
const int e52=e25;
const int e53=e35;
const int e54=e45;
module controller // schedules the algorithm
// algorithm status
status : [0..8];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
turn4 : [0..n_sensors];
turn5 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=5) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=5) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=5) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=5) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=5) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=5) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=2) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=2) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=3) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=3) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=4) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=4) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=5) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=5) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=5) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=5) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=5) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=5) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=1) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=1) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=3) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=3) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=4) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=4) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=5) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=5) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=5) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=5) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=5) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=5) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=1) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=1) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=2) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=2) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=4) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=4) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=5) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=5) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=5) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=5) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=5) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=5) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=1) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=1) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=2) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=2) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=3) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=3) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (turn5'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
[str4] status=2 & turn1=4 -> (status'=2);
[fin4] status=2 & turn1=4 -> (status'=3);
[str5] status=2 & turn1=5 -> (status'=2);
[fin5] status=2 & turn1=5 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
[str4] status=3 & turn2=4 -> (status'=3);
[fin4] status=3 & turn2=4 -> (status'=4);
[str5] status=3 & turn2=5 -> (status'=3);
[fin5] status=3 & turn2=5 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[str4] status=4 & turn3=4 -> (status'=4);
[fin4] status=4 & turn3=4 -> (status'=5);
[str5] status=4 & turn3=5 -> (status'=4);
[fin5] status=4 & turn3=5 -> (status'=5);
// 4th round
[str1] status=5 & turn4=1 -> (status'=5);
[fin1] status=5 & turn4=1 -> (status'=6);
[str2] status=5 & turn4=2 -> (status'=5);
[fin2] status=5 & turn4=2 -> (status'=6);
[str3] status=5 & turn4=3 -> (status'=5);
[fin3] status=5 & turn4=3 -> (status'=6);
[str4] status=5 & turn4=4 -> (status'=5);
[fin4] status=5 & turn4=4 -> (status'=6);
[str5] status=5 & turn4=5 -> (status'=5);
[fin5] status=5 & turn4=5 -> (status'=6);
// 5th round
[str1] status=6 & turn5=1 -> (status'=6);
[fin1] status=6 & turn5=1 -> (status'=7);
[str2] status=6 & turn5=2 -> (status'=6);
[fin2] status=6 & turn5=2 -> (status'=7);
[str3] status=6 & turn5=3 -> (status'=6);
[fin3] status=6 & turn5=3 -> (status'=7);
[str4] status=6 & turn5=4 -> (status'=6);
[fin4] status=6 & turn5=4 -> (status'=7);
[str5] status=6 & turn5=5 -> (status'=6);
[fin5] status=6 & turn5=5 -> (status'=7);
[] status=7 -> (status'=8);
[] status=8 -> (status'=8);
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
module sensor4 = sensor1
[
state1=state4,
str1=str4,
fin1=fin4,
m1_t1=m4_t1,
m1_t2=m4_t2,
m4_t1=m1_t1,
m4_t2=m1_t2,
resource1=resource4,
resource4=resource1,
e12=e42,
e13=e43,
e14=e41,
e15=e45,
e41=e14,
e42=e12,
e43=e13,
e45=e15
]
endmodule
module sensor5 = sensor1
[
state1=state5,
str1=str5,
fin1=fin5,
m1_t1=m5_t1,
m1_t2=m5_t2,
m5_t1=m1_t1,
m5_t2=m1_t2,
resource1=resource5,
resource5=resource1,
e12=e52,
e13=e53,
e14=e54,
e15=e51,
e51=e15,
e52=e12,
e53=e13,
e54=e14
]
endmodule
// formulae for scheduling
formula s1_sched = (turn1=1 | turn2=1 | turn3=1 | turn4=1 | turn5=1);
formula s2_sched = (turn1=2 | turn2=2 | turn3=2 | turn4=2 | turn5=2);
formula s3_sched = (turn1=3 | turn2=3 | turn3=3 | turn4=3 | turn5=3);
formula s4_sched = (turn1=4 | turn2=4 | turn3=4 | turn4=4 | turn5=4);
formula s5_sched = (turn1=5 | turn2=5 | turn3=5 | turn4=5 | turn5=5);
formula all_not_sched = !(s1_sched | s2_sched | s3_sched | s4_sched | s5_sched);
formula all_sched = (s1_sched & s2_sched & s3_sched & s4_sched & s5_sched);
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1+m4_t1+m5_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2+m4_t2+m5_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 + e14*m4_t1 + e15*m5_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 + e14*m4_t2 + e15*m5_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3) | (m4_t1=1 & resource1=resource4) | (m5_t1=1 & resource1=resource5);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3) | (m4_t2=1 & resource1=resource4) | (m5_t2=1 & resource1=resource5);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))+e14*(1-((m4_t1+m4_t2)=0?0:1))+e15*(1-((m5_t1+m5_t2)=0?0:1))) / (e12+e13+e14+e15);
// labels and formulae for property specification
formula finished = (status=7);
label "end" = (status=8);
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
formula agent4_joins_successful_team = (task1_completed & m4_t1=1) | (task2_completed & m4_t2=1);
formula agent4_joins_successful_team_of_1 = (task1_completed & m4_t1=1 & team_size_t1=1) | (task2_completed & m4_t2=1 & team_size_t2=1);
formula agent4_joins_successful_team_of_2 = (task1_completed & m4_t1=1 & team_size_t1=2) | (task2_completed & m4_t2=1 & team_size_t2=2);
formula agent4_joins_successful_team_of_3 = (task1_completed & m4_t1=1 & team_size_t1=3) | (task2_completed & m4_t2=1 & team_size_t2=3);
formula agent5_joins_successful_team = (task1_completed & m5_t1=1) | (task2_completed & m5_t2=1);
formula agent5_joins_successful_team_of_1 = (task1_completed & m5_t1=1 & team_size_t1=1) | (task2_completed & m5_t2=1 & team_size_t2=1);
formula agent5_joins_successful_team_of_2 = (task1_completed & m5_t1=1 & team_size_t1=2) | (task2_completed & m5_t2=1 & team_size_t2=2);
formula agent5_joins_successful_team_of_3 = (task1_completed & m5_t1=1 & team_size_t1=3) | (task2_completed & m5_t2=1 & team_size_t2=3);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)|(m4_t1=1&resource4=1)|(m5_t1=1&resource5=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)|(m4_t1=1&resource4=2)|(m5_t1=1&resource5=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)|(m4_t1=1&resource4=3)|(m5_t1=1&resource5=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)|(m4_t2=1&resource4=1)|(m5_t2=1&resource5=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)|(m4_t2=1&resource4=2)|(m5_t2=1&resource5=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)|(m4_t2=1&resource4=3)|(m5_t2=1&resource5=3)));
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
[] agent4_joins_successful_team : 1;
[] agent5_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

45
examples/multiobjective/mdp/team/origFiles/team.pctl
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// Max probability of completing task 1
"single_task1": Pmax=? [ F task1_completed ]
// Max possible expected W1 (size of successful team)
"single_w1": R{"w_1_total"}max=? [ F "end" ]
// Max possible expected W2 (num tasks completed)
"single_w2": R{"w_2_total"}max=? [ F "end" ]
// Values computed using above queries:
const double q1 =
n_sensors=2 ? 0.9795918367346945 :
n_sensors=3 ? 2.3265306122448983 :
n_sensors=4 ? 2.551020408163265 :
n_sensors=5 ? 2.8979591836734775 :
0.0;
const double q2 =
n_sensors=2 ? 0.7142857142857146 :
n_sensors=3 ? 1.2448979591836744 :
n_sensors=4 ? 1.4285714285714293 :
n_sensors=5 ? 1.6734693877551006 :
0.0;
// Numerical: maximise probability of completing task 1
// with 95% of possible value for expected W1 (size of successful team)
"num_task1": multi(Pmax=? [ F task1_completed ], R{"w_1_total"}>=(0.95*q1) [ F true ])
// Numerical (3-objective): maximise probability of completing task 1
// with 95% of possible value for expected W1 (size of successful team)
// and also at least 0.5 probability of completing task 2
"num_task1_3": multi(Pmax=? [ F task1_completed ], R{"w_1_total"}>=(0.95*q1) [ F true ], P>=0.5 [ F task2_completed ])
// Other numerical queries:
multi(R{"w_1_total"}max=? [ F true ], R{"w_2_total"}>=(0.95*q2) [ F true ])
multi(R{"w_2_total"}max=? [ F true ], R{"w_1_total"}>=(0.95*q1) [ F true ])
// Pareto: maximise probability of completing task 1 and expected W1 (size of successful team)
"pareto": multi(Pmax=? [ F task1_completed ], R{"w_1_total"}max=? [ F true ])
// Pareto (3-objective): maximise probability of completing tasks 1/2 and expected W1 (size of successful team)
"pareto3": multi(Pmax=? [ F task1_completed ], R{"w_1_total"}max=? [ F true ], Pmax=? [ F task2_completed ])

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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 3;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
// network configuration
const int e12=1;
const int e13=1;
const int e21=e12;
const int e23=1;
const int e31=e13;
const int e32=e23;
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))) / (e12+e13);
module controller // schedules the algorithm
// algorithm status
status : [0..6];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/6 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (status'=1)
+ 1/6 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (status'=1)
+ 1/6 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (status'=1)
+ 1/6 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (status'=1)
+ 1/6 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (status'=1)
+ 1/6 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[] status=5 -> (status'=6);
[] status=6 -> true;
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
// labels and formulae for property specification
formula finished = (status=5);
label "end" = (status=6);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)));
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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examples/multiobjective/mdp/team/team2obj_3_numerical.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}>=2.210204082 [ C ])

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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}max=? [ C ])

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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 4;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
const int resource4=1;
// network configuration
const int e12=1;
const int e13=1;
const int e14=1;
const int e21=e12;
const int e23=1;
const int e24=1;
const int e31=e13;
const int e32=e23;
const int e34=1;
const int e41=e14;
const int e42=e24;
const int e43=e34;
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1+m4_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2+m4_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 + e14*m4_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 + e14*m4_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3) | (m4_t1=1 & resource1=resource4);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3) | (m4_t2=1 & resource1=resource4);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))+e14*(1-((m4_t1+m4_t2)=0?0:1))) / (e12+e13+e14);
module controller // schedules the algorithm
// algorithm status
status : [0..7];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
turn4 : [0..n_sensors];
turn5 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/24 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
[str4] status=2 & turn1=4 -> (status'=2);
[fin4] status=2 & turn1=4 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
[str4] status=3 & turn2=4 -> (status'=3);
[fin4] status=3 & turn2=4 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[str4] status=4 & turn3=4 -> (status'=4);
[fin4] status=4 & turn3=4 -> (status'=5);
// 4th round
[str1] status=5 & turn4=1 -> (status'=5);
[fin1] status=5 & turn4=1 -> (status'=6);
[str2] status=5 & turn4=2 -> (status'=5);
[fin2] status=5 & turn4=2 -> (status'=6);
[str3] status=5 & turn4=3 -> (status'=5);
[fin3] status=5 & turn4=3 -> (status'=6);
[str4] status=5 & turn4=4 -> (status'=5);
[fin4] status=5 & turn4=4 -> (status'=6);
[] status=6 -> (status'=7);
[] status=7 -> (status'=7);
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
module sensor4 = sensor1
[
state1=state4,
str1=str4,
fin1=fin4,
m1_t1=m4_t1,
m1_t2=m4_t2,
m4_t1=m1_t1,
m4_t2=m1_t2,
resource1=resource4,
resource4=resource1,
e12=e42,
e13=e43,
e14=e41,
e15=e45,
e41=e14,
e42=e12,
e43=e13,
e45=e15
]
endmodule
// labels and formulae for property specification
formula finished = (status=6);
label "end" = (status=7);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)|(m4_t1=1&resource4=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)|(m4_t1=1&resource4=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)|(m4_t1=1&resource4=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)|(m4_t2=1&resource4=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)|(m4_t2=1&resource4=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)|(m4_t2=1&resource4=3)));
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
formula agent4_joins_successful_team = (task1_completed & m4_t1=1) | (task2_completed & m4_t2=1);
formula agent4_joins_successful_team_of_1 = (task1_completed & m4_t1=1 & team_size_t1=1) | (task2_completed & m4_t2=1 & team_size_t2=1);
formula agent4_joins_successful_team_of_2 = (task1_completed & m4_t1=1 & team_size_t1=2) | (task2_completed & m4_t2=1 & team_size_t2=2);
formula agent4_joins_successful_team_of_3 = (task1_completed & m4_t1=1 & team_size_t1=3) | (task2_completed & m4_t2=1 & team_size_t2=3);
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
[] agent4_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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examples/multiobjective/mdp/team/team2obj_4_numerical.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}>=2.423469388 [ C ])

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examples/multiobjective/mdp/team/team2obj_4_pareto.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}max=? [ C ])

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examples/multiobjective/mdp/team/team2obj_5.nm
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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 5;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
const int resource4=1;
const int resource5=2;
// network configuration
const int e12=1;
const int e13=1;
const int e14=1;
const int e15=1;
const int e21=e12;
const int e23=1;
const int e24=1;
const int e25=1;
const int e31=e13;
const int e32=e23;
const int e34=1;
const int e35=1;
const int e41=e14;
const int e42=e24;
const int e43=e34;
const int e45=1;
const int e51=e15;
const int e52=e25;
const int e53=e35;
const int e54=e45;
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1+m4_t1+m5_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2+m4_t2+m5_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 + e14*m4_t1 + e15*m5_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 + e14*m4_t2 + e15*m5_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3) | (m4_t1=1 & resource1=resource4) | (m5_t1=1 & resource1=resource5);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3) | (m4_t2=1 & resource1=resource4) | (m5_t2=1 & resource1=resource5);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))+e14*(1-((m4_t1+m4_t2)=0?0:1))+e15*(1-((m5_t1+m5_t2)=0?0:1))) / (e12+e13+e14+e15);
module controller // schedules the algorithm
// algorithm status
status : [0..8];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
turn4 : [0..n_sensors];
turn5 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=5) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=5) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=5) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=5) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=5) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=5) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=2) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=2) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=3) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=3) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=4) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=4) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=5) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=5) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=5) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=5) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=5) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=5) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=1) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=1) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=3) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=3) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=4) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=4) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=5) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=5) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=5) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=5) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=5) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=5) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=1) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=1) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=2) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=2) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=4) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=4) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=5) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=5) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=5) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=5) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=5) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=5) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=1) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=1) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=2) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=2) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=3) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=3) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (turn5'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
[str4] status=2 & turn1=4 -> (status'=2);
[fin4] status=2 & turn1=4 -> (status'=3);
[str5] status=2 & turn1=5 -> (status'=2);
[fin5] status=2 & turn1=5 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
[str4] status=3 & turn2=4 -> (status'=3);
[fin4] status=3 & turn2=4 -> (status'=4);
[str5] status=3 & turn2=5 -> (status'=3);
[fin5] status=3 & turn2=5 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[str4] status=4 & turn3=4 -> (status'=4);
[fin4] status=4 & turn3=4 -> (status'=5);
[str5] status=4 & turn3=5 -> (status'=4);
[fin5] status=4 & turn3=5 -> (status'=5);
// 4th round
[str1] status=5 & turn4=1 -> (status'=5);
[fin1] status=5 & turn4=1 -> (status'=6);
[str2] status=5 & turn4=2 -> (status'=5);
[fin2] status=5 & turn4=2 -> (status'=6);
[str3] status=5 & turn4=3 -> (status'=5);
[fin3] status=5 & turn4=3 -> (status'=6);
[str4] status=5 & turn4=4 -> (status'=5);
[fin4] status=5 & turn4=4 -> (status'=6);
[str5] status=5 & turn4=5 -> (status'=5);
[fin5] status=5 & turn4=5 -> (status'=6);
// 5th round
[str1] status=6 & turn5=1 -> (status'=6);
[fin1] status=6 & turn5=1 -> (status'=7);
[str2] status=6 & turn5=2 -> (status'=6);
[fin2] status=6 & turn5=2 -> (status'=7);
[str3] status=6 & turn5=3 -> (status'=6);
[fin3] status=6 & turn5=3 -> (status'=7);
[str4] status=6 & turn5=4 -> (status'=6);
[fin4] status=6 & turn5=4 -> (status'=7);
[str5] status=6 & turn5=5 -> (status'=6);
[fin5] status=6 & turn5=5 -> (status'=7);
[] status=7 -> (status'=8);
[] status=8 -> (status'=8);
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
module sensor4 = sensor1
[
state1=state4,
str1=str4,
fin1=fin4,
m1_t1=m4_t1,
m1_t2=m4_t2,
m4_t1=m1_t1,
m4_t2=m1_t2,
resource1=resource4,
resource4=resource1,
e12=e42,
e13=e43,
e14=e41,
e15=e45,
e41=e14,
e42=e12,
e43=e13,
e45=e15
]
endmodule
module sensor5 = sensor1
[
state1=state5,
str1=str5,
fin1=fin5,
m1_t1=m5_t1,
m1_t2=m5_t2,
m5_t1=m1_t1,
m5_t2=m1_t2,
resource1=resource5,
resource5=resource1,
e12=e52,
e13=e53,
e14=e54,
e15=e51,
e51=e15,
e52=e12,
e53=e13,
e54=e14
]
endmodule
// formulae for scheduling
formula s1_sched = (turn1=1 | turn2=1 | turn3=1 | turn4=1 | turn5=1);
formula s2_sched = (turn1=2 | turn2=2 | turn3=2 | turn4=2 | turn5=2);
formula s3_sched = (turn1=3 | turn2=3 | turn3=3 | turn4=3 | turn5=3);
formula s4_sched = (turn1=4 | turn2=4 | turn3=4 | turn4=4 | turn5=4);
formula s5_sched = (turn1=5 | turn2=5 | turn3=5 | turn4=5 | turn5=5);
formula all_not_sched = !(s1_sched | s2_sched | s3_sched | s4_sched | s5_sched);
formula all_sched = (s1_sched & s2_sched & s3_sched & s4_sched & s5_sched);
// labels and formulae for property specification
formula finished = (status=7);
label "end" = (status=8);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)|(m4_t1=1&resource4=1)|(m5_t1=1&resource5=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)|(m4_t1=1&resource4=2)|(m5_t1=1&resource5=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)|(m4_t1=1&resource4=3)|(m5_t1=1&resource5=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)|(m4_t2=1&resource4=1)|(m5_t2=1&resource5=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)|(m4_t2=1&resource4=2)|(m5_t2=1&resource5=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)|(m4_t2=1&resource4=3)|(m5_t2=1&resource5=3)));
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
formula agent4_joins_successful_team = (task1_completed & m4_t1=1) | (task2_completed & m4_t2=1);
formula agent4_joins_successful_team_of_1 = (task1_completed & m4_t1=1 & team_size_t1=1) | (task2_completed & m4_t2=1 & team_size_t2=1);
formula agent4_joins_successful_team_of_2 = (task1_completed & m4_t1=1 & team_size_t1=2) | (task2_completed & m4_t2=1 & team_size_t2=2);
formula agent4_joins_successful_team_of_3 = (task1_completed & m4_t1=1 & team_size_t1=3) | (task2_completed & m4_t2=1 & team_size_t2=3);
formula agent5_joins_successful_team = (task1_completed & m5_t1=1) | (task2_completed & m5_t2=1);
formula agent5_joins_successful_team_of_1 = (task1_completed & m5_t1=1 & team_size_t1=1) | (task2_completed & m5_t2=1 & team_size_t2=1);
formula agent5_joins_successful_team_of_2 = (task1_completed & m5_t1=1 & team_size_t1=2) | (task2_completed & m5_t2=1 & team_size_t2=2);
formula agent5_joins_successful_team_of_3 = (task1_completed & m5_t1=1 & team_size_t1=3) | (task2_completed & m5_t2=1 & team_size_t2=3);
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
[] agent4_joins_successful_team : 1;
[] agent5_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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examples/multiobjective/mdp/team/team2obj_5_numerical.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}>=2.753061224 [ C ])

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examples/multiobjective/mdp/team/team2obj_5_pareto.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}max=? [ C ])

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examples/multiobjective/mdp/team/team3obj_3.nm
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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 3;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
// network configuration
const int e12=1;
const int e13=1;
const int e21=e12;
const int e23=1;
const int e31=e13;
const int e32=e23;
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))) / (e12+e13);
module controller // schedules the algorithm
// algorithm status
status : [0..6];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/6 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (status'=1)
+ 1/6 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (status'=1)
+ 1/6 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (status'=1)
+ 1/6 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (status'=1)
+ 1/6 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (status'=1)
+ 1/6 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[] status=5 -> (status'=6);
[] status=6 -> true;
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
// labels and formulae for property specification
formula finished = (status=5);
label "end" = (status=6);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)));
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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examples/multiobjective/mdp/team/team3obj_3_numerical.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}>=2.210204082 [ C ], P>=0.5 [ F task2_completed ])

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examples/multiobjective/mdp/team/team3obj_3_pareto.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}max=? [ C ], Pmax=? [ F task2_completed ])

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examples/multiobjective/mdp/team/team3obj_4.nm
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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 4;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
const int resource4=1;
// network configuration
const int e12=1;
const int e13=1;
const int e14=1;
const int e21=e12;
const int e23=1;
const int e24=1;
const int e31=e13;
const int e32=e23;
const int e34=1;
const int e41=e14;
const int e42=e24;
const int e43=e34;
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1+m4_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2+m4_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 + e14*m4_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 + e14*m4_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3) | (m4_t1=1 & resource1=resource4);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3) | (m4_t2=1 & resource1=resource4);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))+e14*(1-((m4_t1+m4_t2)=0?0:1))) / (e12+e13+e14);
module controller // schedules the algorithm
// algorithm status
status : [0..7];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
turn4 : [0..n_sensors];
turn5 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/24 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (status'=1)
+ 1/24 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
[str4] status=2 & turn1=4 -> (status'=2);
[fin4] status=2 & turn1=4 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
[str4] status=3 & turn2=4 -> (status'=3);
[fin4] status=3 & turn2=4 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[str4] status=4 & turn3=4 -> (status'=4);
[fin4] status=4 & turn3=4 -> (status'=5);
// 4th round
[str1] status=5 & turn4=1 -> (status'=5);
[fin1] status=5 & turn4=1 -> (status'=6);
[str2] status=5 & turn4=2 -> (status'=5);
[fin2] status=5 & turn4=2 -> (status'=6);
[str3] status=5 & turn4=3 -> (status'=5);
[fin3] status=5 & turn4=3 -> (status'=6);
[str4] status=5 & turn4=4 -> (status'=5);
[fin4] status=5 & turn4=4 -> (status'=6);
[] status=6 -> (status'=7);
[] status=7 -> (status'=7);
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
module sensor4 = sensor1
[
state1=state4,
str1=str4,
fin1=fin4,
m1_t1=m4_t1,
m1_t2=m4_t2,
m4_t1=m1_t1,
m4_t2=m1_t2,
resource1=resource4,
resource4=resource1,
e12=e42,
e13=e43,
e14=e41,
e15=e45,
e41=e14,
e42=e12,
e43=e13,
e45=e15
]
endmodule
// labels and formulae for property specification
formula finished = (status=6);
label "end" = (status=7);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)|(m4_t1=1&resource4=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)|(m4_t1=1&resource4=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)|(m4_t1=1&resource4=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)|(m4_t2=1&resource4=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)|(m4_t2=1&resource4=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)|(m4_t2=1&resource4=3)));
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
formula agent4_joins_successful_team = (task1_completed & m4_t1=1) | (task2_completed & m4_t2=1);
formula agent4_joins_successful_team_of_1 = (task1_completed & m4_t1=1 & team_size_t1=1) | (task2_completed & m4_t2=1 & team_size_t2=1);
formula agent4_joins_successful_team_of_2 = (task1_completed & m4_t1=1 & team_size_t1=2) | (task2_completed & m4_t2=1 & team_size_t2=2);
formula agent4_joins_successful_team_of_3 = (task1_completed & m4_t1=1 & team_size_t1=3) | (task2_completed & m4_t2=1 & team_size_t2=3);
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
[] agent4_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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examples/multiobjective/mdp/team/team3obj_4_numerical.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}>=2.423469388 [ C ], P>=0.5 [ F task2_completed ])

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examples/multiobjective/mdp/team/team3obj_4_pareto.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}max=? [ C ], Pmax=? [ F task2_completed ])

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examples/multiobjective/mdp/team/team3obj_5.nm
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mdp
// parameters
const int n_resources = 3;
const int n_tasks = 2;
const int n_sensors = 5;
// sensor resources
const int resource1=1;
const int resource2=2;
const int resource3=3;
const int resource4=1;
const int resource5=2;
// network configuration
const int e12=1;
const int e13=1;
const int e14=1;
const int e15=1;
const int e21=e12;
const int e23=1;
const int e24=1;
const int e25=1;
const int e31=e13;
const int e32=e23;
const int e34=1;
const int e35=1;
const int e41=e14;
const int e42=e24;
const int e43=e34;
const int e45=1;
const int e51=e15;
const int e52=e25;
const int e53=e35;
const int e54=e45;
// agent is committed to some team
formula committed = (m1_t1+m1_t2) > 0;
// formulae to compute team sizes
formula team_size_t1 = m1_t1+m2_t1+m3_t1+m4_t1+m5_t1;
formula team_size_t2 = m1_t2+m2_t2+m3_t2+m4_t2+m5_t2;
// formulae to check whether the agent can join the team
formula can_join_t1 = e12*m2_t1 + e13*m3_t1 + e14*m4_t1 + e15*m5_t1 > 0;
formula can_join_t2 = e12*m2_t2 + e13*m3_t2 + e14*m4_t2 + e15*m5_t2 > 0;
// formulae to check whether agent has the resource required by the task
formula has_resource_t1 = ( (t1_r1=1&resource1=1) | (t1_r2=1&resource1=2) | (t1_r3=1&resource1=3) );
formula has_resource_t2 = ( (t2_r1=1&resource1=1) | (t2_r2=1&resource1=2) | (t2_r3=1&resource1=3) );
// formulae to check whether the resource of an agent has been already filled in the team
formula resource_filled_t1 = (m2_t1=1 & resource1=resource2) | (m3_t1=1 & resource1=resource3) | (m4_t1=1 & resource1=resource4) | (m5_t1=1 & resource1=resource5);
formula resource_filled_t2 = (m2_t2=1 & resource1=resource2) | (m3_t2=1 & resource1=resource3) | (m4_t2=1 & resource1=resource4) | (m5_t2=1 & resource1=resource5);
// formula to compute team initiation probability (assuming each agent has at least one connection)
formula IP = (e12*(1-((m2_t1+m2_t2)=0?0:1))+e13*(1-((m3_t1+m3_t2)=0?0:1))+e14*(1-((m4_t1+m4_t2)=0?0:1))+e15*(1-((m5_t1+m5_t2)=0?0:1))) / (e12+e13+e14+e15);
module controller // schedules the algorithm
// algorithm status
status : [0..8];
// task resource indicator variables
t1_r1 : [0..1];
t1_r2 : [0..1];
t1_r3 : [0..1];
t2_r1 : [0..1];
t2_r2 : [0..1];
t2_r3 : [0..1];
// schedule placeholders
turn1 : [0..n_sensors];
turn2 : [0..n_sensors];
turn3 : [0..n_sensors];
turn4 : [0..n_sensors];
turn5 : [0..n_sensors];
// selecting schedule uniformly at random
[] status=0 -> 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=3) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=4) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=5) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=2) & (turn3'=5) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=2) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=4) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=5) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=3) & (turn3'=5) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=2) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=3) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=5) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=4) & (turn3'=5) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=2) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=2) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=3) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=3) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=4) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=1) & (turn2'=5) & (turn3'=4) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=3) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=4) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=5) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=1) & (turn3'=5) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=1) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=4) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=5) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=3) & (turn3'=5) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=1) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=3) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=5) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=4) & (turn3'=5) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=1) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=1) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=3) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=3) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=4) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=2) & (turn2'=5) & (turn3'=4) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=2) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=4) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=5) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=1) & (turn3'=5) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=1) & (turn4'=5) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=4) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=5) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=2) & (turn3'=5) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=1) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=2) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=5) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=4) & (turn3'=5) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=1) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=1) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=2) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=2) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=4) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=3) & (turn2'=5) & (turn3'=4) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=2) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=3) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=5) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=1) & (turn3'=5) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=1) & (turn4'=5) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=3) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=5) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=2) & (turn3'=5) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=1) & (turn4'=5) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (turn5'=5) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=2) & (turn4'=5) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=5) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=3) & (turn3'=5) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=1) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=1) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=2) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=2) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=3) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=4) & (turn2'=5) & (turn3'=3) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=2) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=2) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=3) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=3) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=4) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=1) & (turn3'=4) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=1) & (turn4'=3) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=1) & (turn4'=4) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=3) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=3) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=4) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=2) & (turn3'=4) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=1) & (turn4'=2) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=1) & (turn4'=4) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=2) & (turn4'=1) & (turn5'=4) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=2) & (turn4'=4) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=4) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=3) & (turn3'=4) & (turn4'=2) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=1) & (turn4'=2) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=1) & (turn4'=3) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=2) & (turn4'=1) & (turn5'=3) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=2) & (turn4'=3) & (turn5'=1) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=3) & (turn4'=1) & (turn5'=2) & (status'=1)
+ 1/120 : (turn1'=5) & (turn2'=4) & (turn3'=3) & (turn4'=2) & (turn5'=1) & (status'=1);
// initialising non-empty tasks uniformly at random
[] status=1 -> 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=0) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=0) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=0) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=0) & (t2_r2'=1) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=0) & (t2_r3'=1) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=0) & (status'=2)
+ 1/49 : (t1_r1'=1) & (t1_r2'=1) & (t1_r3'=1) & (t2_r1'=1) & (t2_r2'=1) & (t2_r3'=1) & (status'=2);
// executing the schedule
// 1st round
[str1] status=2 & turn1=1 -> (status'=2);
[fin1] status=2 & turn1=1 -> (status'=3);
[str2] status=2 & turn1=2 -> (status'=2);
[fin2] status=2 & turn1=2 -> (status'=3);
[str3] status=2 & turn1=3 -> (status'=2);
[fin3] status=2 & turn1=3 -> (status'=3);
[str4] status=2 & turn1=4 -> (status'=2);
[fin4] status=2 & turn1=4 -> (status'=3);
[str5] status=2 & turn1=5 -> (status'=2);
[fin5] status=2 & turn1=5 -> (status'=3);
// 2nd round
[str1] status=3 & turn2=1 -> (status'=3);
[fin1] status=3 & turn2=1 -> (status'=4);
[str2] status=3 & turn2=2 -> (status'=3);
[fin2] status=3 & turn2=2 -> (status'=4);
[str3] status=3 & turn2=3 -> (status'=3);
[fin3] status=3 & turn2=3 -> (status'=4);
[str4] status=3 & turn2=4 -> (status'=3);
[fin4] status=3 & turn2=4 -> (status'=4);
[str5] status=3 & turn2=5 -> (status'=3);
[fin5] status=3 & turn2=5 -> (status'=4);
// 3rd round
[str1] status=4 & turn3=1 -> (status'=4);
[fin1] status=4 & turn3=1 -> (status'=5);
[str2] status=4 & turn3=2 -> (status'=4);
[fin2] status=4 & turn3=2 -> (status'=5);
[str3] status=4 & turn3=3 -> (status'=4);
[fin3] status=4 & turn3=3 -> (status'=5);
[str4] status=4 & turn3=4 -> (status'=4);
[fin4] status=4 & turn3=4 -> (status'=5);
[str5] status=4 & turn3=5 -> (status'=4);
[fin5] status=4 & turn3=5 -> (status'=5);
// 4th round
[str1] status=5 & turn4=1 -> (status'=5);
[fin1] status=5 & turn4=1 -> (status'=6);
[str2] status=5 & turn4=2 -> (status'=5);
[fin2] status=5 & turn4=2 -> (status'=6);
[str3] status=5 & turn4=3 -> (status'=5);
[fin3] status=5 & turn4=3 -> (status'=6);
[str4] status=5 & turn4=4 -> (status'=5);
[fin4] status=5 & turn4=4 -> (status'=6);
[str5] status=5 & turn4=5 -> (status'=5);
[fin5] status=5 & turn4=5 -> (status'=6);
// 5th round
[str1] status=6 & turn5=1 -> (status'=6);
[fin1] status=6 & turn5=1 -> (status'=7);
[str2] status=6 & turn5=2 -> (status'=6);
[fin2] status=6 & turn5=2 -> (status'=7);
[str3] status=6 & turn5=3 -> (status'=6);
[fin3] status=6 & turn5=3 -> (status'=7);
[str4] status=6 & turn5=4 -> (status'=6);
[fin4] status=6 & turn5=4 -> (status'=7);
[str5] status=6 & turn5=5 -> (status'=6);
[fin5] status=6 & turn5=5 -> (status'=7);
[] status=7 -> (status'=8);
[] status=8 -> (status'=8);
endmodule
module sensor1
state1 : [0..1];
// team membership indicators
m1_t1 : [0..1];
m1_t2 : [0..1];
// starting turn, selecting order of tasks
[str1] state1=0 -> (state1'=1);
// if there is no team and has required skill - initiating the team
[] state1=1 & !committed & team_size_t1=0 & has_resource_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2=0 & has_resource_t2 -> (m1_t2'=1);
// if team already exists and one of the neighbours is in it - joining the team
[] state1=1 & !committed & team_size_t1>0 & can_join_t1 & has_resource_t1 & !resource_filled_t1 -> (m1_t1'=1);
[] state1=1 & !committed & team_size_t2>0 & can_join_t2 & has_resource_t2 & !resource_filled_t2 -> (m1_t2'=1);
[fin1] state1>0 -> (state1'=0);
endmodule
module sensor2 = sensor1
[
state1=state2,
str1=str2,
fin1=fin2,
m1_t1=m2_t1,
m1_t2=m2_t2,
m2_t1=m1_t1,
m2_t2=m1_t2,
resource1=resource2,
resource2=resource1,
e12=e21,
e13=e23,
e14=e24,
e15=e25,
e21=e12,
e23=e13,
e24=e14,
e25=e15
]
endmodule
module sensor3 = sensor1
[
state1=state3,
str1=str3,
fin1=fin3,
m1_t1=m3_t1,
m1_t2=m3_t2,
m3_t1=m1_t1,
m3_t2=m1_t2,
resource1=resource3,
resource3=resource1,
e12=e32,
e13=e31,
e14=e34,
e15=e35,
e31=e13,
e32=e12,
e34=e14,
e35=e15
]
endmodule
module sensor4 = sensor1
[
state1=state4,
str1=str4,
fin1=fin4,
m1_t1=m4_t1,
m1_t2=m4_t2,
m4_t1=m1_t1,
m4_t2=m1_t2,
resource1=resource4,
resource4=resource1,
e12=e42,
e13=e43,
e14=e41,
e15=e45,
e41=e14,
e42=e12,
e43=e13,
e45=e15
]
endmodule
module sensor5 = sensor1
[
state1=state5,
str1=str5,
fin1=fin5,
m1_t1=m5_t1,
m1_t2=m5_t2,
m5_t1=m1_t1,
m5_t2=m1_t2,
resource1=resource5,
resource5=resource1,
e12=e52,
e13=e53,
e14=e54,
e15=e51,
e51=e15,
e52=e12,
e53=e13,
e54=e14
]
endmodule
// formulae for scheduling
formula s1_sched = (turn1=1 | turn2=1 | turn3=1 | turn4=1 | turn5=1);
formula s2_sched = (turn1=2 | turn2=2 | turn3=2 | turn4=2 | turn5=2);
formula s3_sched = (turn1=3 | turn2=3 | turn3=3 | turn4=3 | turn5=3);
formula s4_sched = (turn1=4 | turn2=4 | turn3=4 | turn4=4 | turn5=4);
formula s5_sched = (turn1=5 | turn2=5 | turn3=5 | turn4=5 | turn5=5);
formula all_not_sched = !(s1_sched | s2_sched | s3_sched | s4_sched | s5_sched);
formula all_sched = (s1_sched & s2_sched & s3_sched & s4_sched & s5_sched);
// labels and formulae for property specification
formula finished = (status=7);
label "end" = (status=8);
formula task1_completed = finished
& ((t1_r1=1)=>((m1_t1=1&resource1=1)|(m2_t1=1&resource2=1)|(m3_t1=1&resource3=1)|(m4_t1=1&resource4=1)|(m5_t1=1&resource5=1)))
& ((t1_r2=1)=>((m1_t1=1&resource1=2)|(m2_t1=1&resource2=2)|(m3_t1=1&resource3=2)|(m4_t1=1&resource4=2)|(m5_t1=1&resource5=2)))
& ((t1_r3=1)=>((m1_t1=1&resource1=3)|(m2_t1=1&resource2=3)|(m3_t1=1&resource3=3)|(m4_t1=1&resource4=3)|(m5_t1=1&resource5=3)));
formula task2_completed = finished
& ((t2_r1=1)=>((m1_t2=1&resource1=1)|(m2_t2=1&resource2=1)|(m3_t2=1&resource3=1)|(m4_t2=1&resource4=1)|(m5_t2=1&resource5=1)))
& ((t2_r2=1)=>((m1_t2=1&resource1=2)|(m2_t2=1&resource2=2)|(m3_t2=1&resource3=2)|(m4_t2=1&resource4=2)|(m5_t2=1&resource5=2)))
& ((t2_r3=1)=>((m1_t2=1&resource1=3)|(m2_t2=1&resource2=3)|(m3_t2=1&resource3=3)|(m4_t2=1&resource4=3)|(m5_t2=1&resource5=3)));
formula agent1_joins_successful_team = (task1_completed & m1_t1=1) | (task2_completed & m1_t2=1);
formula agent1_joins_successful_team_of_1 = (task1_completed & m1_t1=1 & team_size_t1=1) | (task2_completed & m1_t2=1 & team_size_t2=1);
formula agent1_joins_successful_team_of_2 = (task1_completed & m1_t1=1 & team_size_t1=2) | (task2_completed & m1_t2=1 & team_size_t2=2);
formula agent1_joins_successful_team_of_3 = (task1_completed & m1_t1=1 & team_size_t1=3) | (task2_completed & m1_t2=1 & team_size_t2=3);
formula agent2_joins_successful_team = (task1_completed & m2_t1=1) | (task2_completed & m2_t2=1);
formula agent2_joins_successful_team_of_1 = (task1_completed & m2_t1=1 & team_size_t1=1) | (task2_completed & m2_t2=1 & team_size_t2=1);
formula agent2_joins_successful_team_of_2 = (task1_completed & m2_t1=1 & team_size_t1=2) | (task2_completed & m2_t2=1 & team_size_t2=2);
formula agent2_joins_successful_team_of_3 = (task1_completed & m2_t1=1 & team_size_t1=3) | (task2_completed & m2_t2=1 & team_size_t2=3);
formula agent3_joins_successful_team = (task1_completed & m3_t1=1) | (task2_completed & m3_t2=1);
formula agent3_joins_successful_team_of_1 = (task1_completed & m3_t1=1 & team_size_t1=1) | (task2_completed & m3_t2=1 & team_size_t2=1);
formula agent3_joins_successful_team_of_2 = (task1_completed & m3_t1=1 & team_size_t1=2) | (task2_completed & m3_t2=1 & team_size_t2=2);
formula agent3_joins_successful_team_of_3 = (task1_completed & m3_t1=1 & team_size_t1=3) | (task2_completed & m3_t2=1 & team_size_t2=3);
formula agent4_joins_successful_team = (task1_completed & m4_t1=1) | (task2_completed & m4_t2=1);
formula agent4_joins_successful_team_of_1 = (task1_completed & m4_t1=1 & team_size_t1=1) | (task2_completed & m4_t2=1 & team_size_t2=1);
formula agent4_joins_successful_team_of_2 = (task1_completed & m4_t1=1 & team_size_t1=2) | (task2_completed & m4_t2=1 & team_size_t2=2);
formula agent4_joins_successful_team_of_3 = (task1_completed & m4_t1=1 & team_size_t1=3) | (task2_completed & m4_t2=1 & team_size_t2=3);
formula agent5_joins_successful_team = (task1_completed & m5_t1=1) | (task2_completed & m5_t2=1);
formula agent5_joins_successful_team_of_1 = (task1_completed & m5_t1=1 & team_size_t1=1) | (task2_completed & m5_t2=1 & team_size_t2=1);
formula agent5_joins_successful_team_of_2 = (task1_completed & m5_t1=1 & team_size_t1=2) | (task2_completed & m5_t2=1 & team_size_t2=2);
formula agent5_joins_successful_team_of_3 = (task1_completed & m5_t1=1 & team_size_t1=3) | (task2_completed & m5_t2=1 & team_size_t2=3);
// rewards
rewards "w_1_total"
[] agent1_joins_successful_team : 1;
[] agent2_joins_successful_team : 1;
[] agent3_joins_successful_team : 1;
[] agent4_joins_successful_team : 1;
[] agent5_joins_successful_team : 1;
endrewards
rewards "w_2_total"
[] task1_completed : 1;
[] task2_completed : 1;
endrewards

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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}>=2.753061224 [ C ], P>=0.5 [ F task2_completed ])

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examples/multiobjective/mdp/team/team3obj_5_pareto.pctl
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multi(Pmax=? [ F task1_completed ], R{"w_1_total"}max=? [ C ], Pmax=? [ F task2_completed ])

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// IPv4: PTA model with digitial clocks
// multi-objective model of the host
// gxn/dxp 28/09/09
mdp
//-------------------------------------------------------------
// VARIABLES
const int N=20; // number of abstract hosts
const int K=2; // number of probes to send
// PROBABILITIES
const double old = N/65024; // probability pick an ip address being used
//const double old = 1/2; // probability pick an ip address being used
const double new = (1-old); // probability pick a new ip address
// TIMING CONSTANTS
const int CONSEC = 2; // time interval between sending consecutive probles
const int TRANSTIME = 1; // upper bound on transmission time delay
const int LONGWAIT = 60; // minimum time delay after a high number of address collisions
const int DEFEND = 10;
const int TIME_MAX_X = 60; // max value of clock x
const int TIME_MAX_Y = 10; // max value of clock y
const int TIME_MAX_Z = 1; // max value of clock z
// OTHER CONSTANTS
const int MAXCOLL = 10; // maximum number of collisions before long wait
//-------------------------------------------------------------
// CONCRETE HOST
module host0
x : [0..TIME_MAX_X]; // first clock of the host
y : [0..TIME_MAX_Y]; // second clock of the host
coll : [0..MAXCOLL]; // number of address collisions
probes : [0..K]; // counter (number of probes sent)
mess : [0..1]; // need to send a message or not
defend : [0..1]; // defend (if =1, try to defend IP address)
ip : [1..2]; // ip address (1 - in use & 2 - fresh)
l : [0..4] init 1; // location
// 0 : RECONFIGURE
// 1 : RANDOM
// 2 : WAITSP
// 3 : WAITSG
// 4 : USE
// RECONFIGURE
[reset] l=0 -> (l'=1);
// RANDOM (choose IP address)
[rec0] (l=1) -> true; // get message (ignore since have no ip address)
[rec1] (l=1) -> true; // get message (ignore since have no ip address)
// small number of collisions (choose straight away)
[] l=1 & coll<MAXCOLL -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=1)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=2)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=0)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=1)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=2);
// large number of collisions: (wait for LONGWAIT)
[time] l=1 & coll=MAXCOLL & x<LONGWAIT -> (x'=min(x+1,TIME_MAX_X));
[] l=1 & coll=MAXCOLL & x=LONGWAIT -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=1)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=2)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=0)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=1)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=2);
// WAITSP
// let time pass
[time] l=2 & x<2 -> (x'=min(x+1,2));
// send probe
[send1] l=2 & ip=1 & x=2 & probes<K -> (x'=0) & (probes'=probes+1);
[send2] l=2 & ip=2 & x=2 & probes<K -> (x'=0) & (probes'=probes+1);
// sent K probes and waited 2 seconds
[configured] l=2 & x=2 & probes=K -> (l'=3) & (probes'=0) & (coll'=0) & (x'=0);
// get message and ip does not match: ignore
[rec0] l=2 & ip!=0 -> (l'=l);
[rec1] l=2 & ip!=1 -> (l'=l);
// get a message with matching ip: reconfigure
[rec1] l=2 & ip=1 -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0);
// WAITSG (sends two gratuitious arp probes)
// time passage
[time] l=3 & mess=0 & defend=0 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X));
[time] l=3 & mess=0 & defend=1 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X)) & (y'=min(y+1,DEFEND));
// receive message and same ip: defend
[rec1] l=3 & mess=0 & ip=1 & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0);
// receive message and same ip: defer
[rec1] l=3 & mess=0 & ip=1 & (defend=0 | y<DEFEND) -> (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0);
// receive message and different ip
[rec0] l=3 & mess=0 & ip!=0 -> (l'=l);
[rec1] l=3 & mess=0 & ip!=1 -> (l'=l);
// send probe reply or message for defence
[send1] l=3 & ip=1 & mess=1 -> (mess'=0);
[send2] l=3 & ip=2 & mess=1 -> (mess'=0);
// send first gratuitous arp message
[send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1);
[send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1);
// send second gratuitous arp message (move to use)
[send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0);
[send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0);
// USE (only interested in reaching this state so do not need to add anything here)
[] l=4 -> true;
endmodule
//-------------------------------------------------------------
// error automaton for the environment assumption
// do not get a reply when K probes are sent
const int M; // time between sending and receiving a message
module env_error2
env : [0..1]; // 0 active and 1 done
k : [0..2]; // counts the number of messages sent
c1 : [0..M+1]; // time since first message
c2 : [0..M+1]; // time since second message
error : [0..1];
// message with new ip address arrives so done
[send2] error=0 & env=0 -> (env'=1);
// message with old ip address arrives so count
[send1] error=0 & env=0 -> (k'=min(k+1,K));
// time passgae so update relevant clocks
[time] error=0 & env=0 & k=0 -> true;
[time] error=0 & env=0 & k=1 & min(c1,c2)<M -> (c1'=min(c1+1,M+1));
[time] error=0 & env=0 & k=2 & min(c1,c2)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1));
// all clocks reached their bound so an error
[time] error=0 & env=0 & min(c1,c2)=M -> (error'=1);
// send a reply (then done)
[rec1] error=0 & env=0 & k>0 & min(c1,c2)<=M -> (env'=1);
// finished so any action can be performed
[time] error=1 | env=1 -> true;
[send1] error=1 | env=1 -> true;
[send2] error=1 | env=1 -> true;
[rec1] error=1 | env=1 -> true;
endmodule
//-------------------------------------------------------------
// error automaton for the time bounded assumption
// host does not send configured signal within T seconds
const int T;
module time_error
time_error : [0..1];
done : [0..1];
t : [0..T];
[time] t<T-1 & done=0 & time_error=0 -> (t'=t+1); // time passes and bound not reached
[time] t=T-1 & done=0 & time_error=0 -> (time_error'=1); // bound reached so error
[configured] time_error=0 -> (done'=1); // configured within the time bound
// when in error or done state can loop with either action
[configured] time_error=1 | done=1 -> true;
[time] time_error=1 | done=1 -> true;
endmodule

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// IPv4: PTA model with digitial clocks
// multi-objective model of the host
// gxn/dxp 28/09/09
mdp
//-------------------------------------------------------------
// VARIABLES
const int N=20; // number of abstract hosts
const int K=4; // number of probes to send
// PROBABILITIES
const double old = N/65024; // probability pick an ip address being used
//const double old = 0.5; // probability pick an ip address being used
const double new = (1-old); // probability pick a new ip address
// TIMING CONSTANTS
const int CONSEC = 2; // time interval between sending consecutive probles
const int TRANSTIME = 1; // upper bound on transmission time delay
const int LONGWAIT = 60; // minimum time delay after a high number of address collisions
const int DEFEND = 10;
const int TIME_MAX_X = 60; // max value of clock x
const int TIME_MAX_Y = 10; // max value of clock y
const int TIME_MAX_Z = 1; // max value of clock z
// OTHER CONSTANTS
const int MAXCOLL = 10; // maximum number of collisions before long wait
//-------------------------------------------------------------
// CONCRETE HOST
module host0
x : [0..TIME_MAX_X]; // first clock of the host
y : [0..TIME_MAX_Y]; // second clock of the host
coll : [0..MAXCOLL]; // number of address collisions
probes : [0..K]; // counter (number of probes sent)
mess : [0..1]; // need to send a message or not
defend : [0..1]; // defend (if =1, try to defend IP address)
ip : [1..2]; // ip address (1 - in use & 2 - fresh)
l : [0..4] init 1; // location
// 0 : RECONFIGURE
// 1 : RANDOM
// 2 : WAITSP
// 3 : WAITSG
// 4 : USE
// RECONFIGURE
[reset] l=0 -> (l'=1);
// RANDOM (choose IP address)
[rec0] (l=1) -> true; // get message (ignore since have no ip address)
[rec1] (l=1) -> true; // get message (ignore since have no ip address)
// small number of collisions (choose straight away)
[] l=1 & coll<MAXCOLL -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=1)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=2)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=0)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=1)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=2);
// large number of collisions: (wait for LONGWAIT)
[time] l=1 & coll=MAXCOLL & x<LONGWAIT -> (x'=min(x+1,TIME_MAX_X));
[] l=1 & coll=MAXCOLL & x=LONGWAIT -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=1)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=2)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=0)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=1)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=2);
// WAITSP
// let time pass
[time] l=2 & x<2 -> (x'=min(x+1,2));
// send probe
[send1] l=2 & ip=1 & x=2 & probes<K -> (x'=0) & (probes'=probes+1);
[send2] l=2 & ip=2 & x=2 & probes<K -> (x'=0) & (probes'=probes+1);
// sent K probes and waited 2 seconds
[configured] l=2 & x=2 & probes=K -> (l'=3) & (probes'=0) & (coll'=0) & (x'=0);
// get message and ip does not match: ignore
[rec0] l=2 & ip!=0 -> (l'=l);
[rec1] l=2 & ip!=1 -> (l'=l);
// get a message with matching ip: reconfigure
[rec1] l=2 & ip=1 -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0);
// WAITSG (sends two gratuitious arp probes)
// time passage
[time] l=3 & mess=0 & defend=0 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X));
[time] l=3 & mess=0 & defend=1 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X)) & (y'=min(y+1,DEFEND));
// receive message and same ip: defend
[rec1] l=3 & mess=0 & ip=1 & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0);
// receive message and same ip: defer
[rec1] l=3 & mess=0 & ip=1 & (defend=0 | y<DEFEND) -> (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0);
// receive message and different ip
[rec0] l=3 & mess=0 & ip!=0 -> (l'=l);
[rec1] l=3 & mess=0 & ip!=1 -> (l'=l);
// send probe reply or message for defence
[send1] l=3 & ip=1 & mess=1 -> (mess'=0);
[send2] l=3 & ip=2 & mess=1 -> (mess'=0);
// send first gratuitous arp message
[send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1);
[send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1);
// send second gratuitous arp message (move to use)
[send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0);
[send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0);
// USE (only interested in reaching this state so do not need to add anything here)
[] l=4 -> true;
endmodule
//-------------------------------------------------------------
// error automaton for the environment assumption
// do not get a reply when K probes are sent
const int M; // time between sending and receiving a message
module env_error4
env : [0..1]; // 0 active and 1 done
k : [0..4]; // counts the number of messages sent
c1 : [0..M+1]; // time since first message
c2 : [0..M+1]; // time since second message
c3 : [0..M+1]; // time since third message
c4 : [0..M+1]; // time since fourth message
error : [0..1];
// message with new ip address arrives so done
[send2] error=0 & env=0 -> (env'=1);
// message with old ip address arrives so count
[send1] error=0 & env=0 -> (k'=min(k+1,K));
// time passgae so update relevant clocks
[time] error=0 & env=0 & k=0 -> true;
[time] error=0 & env=0 & k=1 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1));
[time] error=0 & env=0 & k=2 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1));
[time] error=0 & env=0 & k=3 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1)) & (c3'=min(c3+1,M+1));
[time] error=0 & env=0 & k=4 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1)) & (c3'=min(c3+1,M+1)) & (c4'=min(c4+1,M+1));
// all clocks reached their bound so an error
[time] error=0 & env=0 & min(c1,c2,c3,c4)=M -> (error'=1);
// send a reply (then done)
[rec1] error=0 & env=0 & k>0 & min(c1,c2,c3,c4)<=M -> (env'=1);
// finished so any action can be performed
[time] error=1 | env=1 -> true;
[send1] error=1 | env=1 -> true;
[send2] error=1 | env=1 -> true;
[send2] error=1 | env=1 -> true;
[rec1] error=1 | env=1 -> true;
endmodule
//-------------------------------------------------------------
// error automaton for the time bounded assumption
// host does not send configured signal within T seconds
const int T;
module time_error
time_error : [0..1];
done : [0..1];
t : [0..T];
[time] t<T-1 & done=0 & time_error=0 -> (t'=t+1); // time passes and bound not reached
[time] t=T-1 & done=0 & time_error=0 -> (time_error'=1); // bound reached so error
[configured] time_error=0 -> (done'=1); // configured within the time bound
// when in error or done state can loop with either action
[configured] time_error=1 | done=1 -> true;
[time] time_error=1 | done=1 -> true;
endmodule

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examples/multiobjective/mdp/zeroconf-tb/origFiles/zeroconf_host_multi_time.pctl
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// Max probability of component violating assumption property (checked separately)
const double p_fail =
K=2 ? 0.19 :
K=4 ? 0.006859000000000001 :
K=6 ? 2.476099000000001E-4 :
K=8 ? 8.938717390000006E-6 :
0;
// Assume-guarantee check via multi-objective
"num_ag": multi(Pmax=? [ F time_error=1 ] , P>=1-p_fail [ G (error=0) ])
// Pareto query for assume-guarantee check
"pareto": multi(Pmax=? [ F time_error=1 ] , Pmax=? [ G (error=0) ])

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examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb2_14.nm
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// IPv4: PTA model with digitial clocks
// multi-objective model of the host
// gxn/dxp 28/09/09
mdp
//-------------------------------------------------------------
// VARIABLES
const int N=20; // number of abstract hosts
const int K=2; // number of probes to send
// PROBABILITIES
const double old = N/65024; // probability pick an ip address being used
//const double old = 1/2; // probability pick an ip address being used
const double new = (1-old); // probability pick a new ip address
// TIMING CONSTANTS
const int CONSEC = 2; // time interval between sending consecutive probles
const int TRANSTIME = 1; // upper bound on transmission time delay
const int LONGWAIT = 60; // minimum time delay after a high number of address collisions
const int DEFEND = 10;
const int TIME_MAX_X = 60; // max value of clock x
const int TIME_MAX_Y = 10; // max value of clock y
const int TIME_MAX_Z = 1; // max value of clock z
// OTHER CONSTANTS
const int MAXCOLL = 10; // maximum number of collisions before long wait
const int M=1; // time between sending and receiving a message
const int T=14;
//-------------------------------------------------------------
// CONCRETE HOST
module host0
x : [0..TIME_MAX_X]; // first clock of the host
y : [0..TIME_MAX_Y]; // second clock of the host
coll : [0..MAXCOLL]; // number of address collisions
probes : [0..K]; // counter (number of probes sent)
mess : [0..1]; // need to send a message or not
defend : [0..1]; // defend (if =1, try to defend IP address)
ip : [1..2]; // ip address (1 - in use & 2 - fresh)
l : [0..4] init 1; // location
// 0 : RECONFIGURE
// 1 : RANDOM
// 2 : WAITSP
// 3 : WAITSG
// 4 : USE
// RECONFIGURE
[reset] l=0 -> (l'=1);
// RANDOM (choose IP address)
[rec0] (l=1) -> true; // get message (ignore since have no ip address)
[rec1] (l=1) -> true; // get message (ignore since have no ip address)
// small number of collisions (choose straight away)
[] l=1 & coll<MAXCOLL -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=1)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=2)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=0)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=1)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=2);
// large number of collisions: (wait for LONGWAIT)
[time] l=1 & coll=MAXCOLL & x<LONGWAIT -> (x'=min(x+1,TIME_MAX_X));
[] l=1 & coll=MAXCOLL & x=LONGWAIT -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=1)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=2)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=0)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=1)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=2);
// WAITSP
// let time pass
[time] l=2 & x<2 -> (x'=min(x+1,2));
// send probe
[send1] l=2 & ip=1 & x=2 & probes<K -> (x'=0) & (probes'=probes+1);
[send2] l=2 & ip=2 & x=2 & probes<K -> (x'=0) & (probes'=probes+1);
// sent K probes and waited 2 seconds
[configured] l=2 & x=2 & probes=K -> (l'=3) & (probes'=0) & (coll'=0) & (x'=0);
// get message and ip does not match: ignore
[rec0] l=2 & ip!=0 -> (l'=l);
[rec1] l=2 & ip!=1 -> (l'=l);
// get a message with matching ip: reconfigure
[rec1] l=2 & ip=1 -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0);
// WAITSG (sends two gratuitious arp probes)
// time passage
[time] l=3 & mess=0 & defend=0 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X));
[time] l=3 & mess=0 & defend=1 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X)) & (y'=min(y+1,DEFEND));
// receive message and same ip: defend
[rec1] l=3 & mess=0 & ip=1 & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0);
// receive message and same ip: defer
[rec1] l=3 & mess=0 & ip=1 & (defend=0 | y<DEFEND) -> (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0);
// receive message and different ip
[rec0] l=3 & mess=0 & ip!=0 -> (l'=l);
[rec1] l=3 & mess=0 & ip!=1 -> (l'=l);
// send probe reply or message for defence
[send1] l=3 & ip=1 & mess=1 -> (mess'=0);
[send2] l=3 & ip=2 & mess=1 -> (mess'=0);
// send first gratuitous arp message
[send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1);
[send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1);
// send second gratuitous arp message (move to use)
[send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0);
[send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0);
// USE (only interested in reaching this state so do not need to add anything here)
[] l=4 -> true;
endmodule
//-------------------------------------------------------------
// error automaton for the environment assumption
// do not get a reply when K probes are sent
module env_error2
env : [0..1]; // 0 active and 1 done
k : [0..2]; // counts the number of messages sent
c1 : [0..M+1]; // time since first message
c2 : [0..M+1]; // time since second message
error : [0..1];
// message with new ip address arrives so done
[send2] error=0 & env=0 -> (env'=1);
// message with old ip address arrives so count
[send1] error=0 & env=0 -> (k'=min(k+1,K));
// time passgae so update relevant clocks
[time] error=0 & env=0 & k=0 -> true;
[time] error=0 & env=0 & k=1 & min(c1,c2)<M -> (c1'=min(c1+1,M+1));
[time] error=0 & env=0 & k=2 & min(c1,c2)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1));
// all clocks reached their bound so an error
[time] error=0 & env=0 & min(c1,c2)=M -> (error'=1);
// send a reply (then done)
[rec1] error=0 & env=0 & k>0 & min(c1,c2)<=M -> (env'=1);
// finished so any action can be performed
[time] error=1 | env=1 -> true;
[send1] error=1 | env=1 -> true;
[send2] error=1 | env=1 -> true;
[rec1] error=1 | env=1 -> true;
endmodule
//-------------------------------------------------------------
// error automaton for the time bounded assumption
// host does not send configured signal within T seconds
module time_error
time_error : [0..1];
done : [0..1];
t : [0..T];
[time] t<T-1 & done=0 & time_error=0 -> (t'=t+1); // time passes and bound not reached
[time] t=T-1 & done=0 & time_error=0 -> (time_error'=1); // bound reached so error
[configured] time_error=0 -> (done'=1); // configured within the time bound
// when in error or done state can loop with either action
[configured] time_error=1 | done=1 -> true;
[time] time_error=1 | done=1 -> true;
endmodule

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examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb2_14_numerical.pctl
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multi(Pmax=? [ F time_error=1 ] , P>=0.81[ G (error=0) ])

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examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb2_14_pareto.pctl
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multi(Pmax=? [ F time_error=1 ] , Pmax=? [ G (error=0) ])

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// IPv4: PTA model with digitial clocks
// multi-objective model of the host
// gxn/dxp 28/09/09
mdp
//-------------------------------------------------------------
// VARIABLES
const int N=20; // number of abstract hosts
const int K=4; // number of probes to send
// PROBABILITIES
const double old = N/65024; // probability pick an ip address being used
//const double old = 0.5; // probability pick an ip address being used
const double new = (1-old); // probability pick a new ip address
// TIMING CONSTANTS
const int CONSEC = 2; // time interval between sending consecutive probles
const int TRANSTIME = 1; // upper bound on transmission time delay
const int LONGWAIT = 60; // minimum time delay after a high number of address collisions
const int DEFEND = 10;
const int TIME_MAX_X = 60; // max value of clock x
const int TIME_MAX_Y = 10; // max value of clock y
const int TIME_MAX_Z = 1; // max value of clock z
// OTHER CONSTANTS
const int MAXCOLL = 10; // maximum number of collisions before long wait
const int M=1; // time between sending and receiving a message
const int T=10;
//-------------------------------------------------------------
// CONCRETE HOST
module host0
x : [0..TIME_MAX_X]; // first clock of the host
y : [0..TIME_MAX_Y]; // second clock of the host
coll : [0..MAXCOLL]; // number of address collisions
probes : [0..K]; // counter (number of probes sent)
mess : [0..1]; // need to send a message or not
defend : [0..1]; // defend (if =1, try to defend IP address)
ip : [1..2]; // ip address (1 - in use & 2 - fresh)
l : [0..4] init 1; // location
// 0 : RECONFIGURE
// 1 : RANDOM
// 2 : WAITSP
// 3 : WAITSG
// 4 : USE
// RECONFIGURE
[reset] l=0 -> (l'=1);
// RANDOM (choose IP address)
[rec0] (l=1) -> true; // get message (ignore since have no ip address)
[rec1] (l=1) -> true; // get message (ignore since have no ip address)
// small number of collisions (choose straight away)
[] l=1 & coll<MAXCOLL -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=1)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=2)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=0)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=1)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=2);
// large number of collisions: (wait for LONGWAIT)
[time] l=1 & coll=MAXCOLL & x<LONGWAIT -> (x'=min(x+1,TIME_MAX_X));
[] l=1 & coll=MAXCOLL & x=LONGWAIT -> 1/3*old : (l'=2) & (ip'=1) & (x'=0)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=1)
+ 1/3*old : (l'=2) & (ip'=1) & (x'=2)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=0)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=1)
+ 1/3*new : (l'=2) & (ip'=2) & (x'=2);
// WAITSP
// let time pass
[time] l=2 & x<2 -> (x'=min(x+1,2));
// send probe
[send1] l=2 & ip=1 & x=2 & probes<K -> (x'=0) & (probes'=probes+1);
[send2] l=2 & ip=2 & x=2 & probes<K -> (x'=0) & (probes'=probes+1);
// sent K probes and waited 2 seconds
[configured] l=2 & x=2 & probes=K -> (l'=3) & (probes'=0) & (coll'=0) & (x'=0);
// get message and ip does not match: ignore
[rec0] l=2 & ip!=0 -> (l'=l);
[rec1] l=2 & ip!=1 -> (l'=l);
// get a message with matching ip: reconfigure
[rec1] l=2 & ip=1 -> (l'=0) & (coll'=min(coll+1,MAXCOLL)) & (x'=0) & (probes'=0);
// WAITSG (sends two gratuitious arp probes)
// time passage
[time] l=3 & mess=0 & defend=0 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X));
[time] l=3 & mess=0 & defend=1 & x<CONSEC -> (x'=min(x+1,TIME_MAX_X)) & (y'=min(y+1,DEFEND));
// receive message and same ip: defend
[rec1] l=3 & mess=0 & ip=1 & (defend=0 | y>=DEFEND) -> (defend'=1) & (mess'=1) & (y'=0);
// receive message and same ip: defer
[rec1] l=3 & mess=0 & ip=1 & (defend=0 | y<DEFEND) -> (l'=0) & (probes'=0) & (defend'=0) & (x'=0) & (y'=0);
// receive message and different ip
[rec0] l=3 & mess=0 & ip!=0 -> (l'=l);
[rec1] l=3 & mess=0 & ip!=1 -> (l'=l);
// send probe reply or message for defence
[send1] l=3 & ip=1 & mess=1 -> (mess'=0);
[send2] l=3 & ip=2 & mess=1 -> (mess'=0);
// send first gratuitous arp message
[send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1);
[send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes<1 -> (x'=0) & (probes'=probes+1);
// send second gratuitous arp message (move to use)
[send1] l=3 & ip=1 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0);
[send2] l=3 & ip=2 & mess=0 & x=CONSEC & probes=1 -> (l'=4) & (x'=0) & (y'=0) & (probes'=0);
// USE (only interested in reaching this state so do not need to add anything here)
[] l=4 -> true;
endmodule
//-------------------------------------------------------------
// error automaton for the environment assumption
// do not get a reply when K probes are sent
module env_error4
env : [0..1]; // 0 active and 1 done
k : [0..4]; // counts the number of messages sent
c1 : [0..M+1]; // time since first message
c2 : [0..M+1]; // time since second message
c3 : [0..M+1]; // time since third message
c4 : [0..M+1]; // time since fourth message
error : [0..1];
// message with new ip address arrives so done
[send2] error=0 & env=0 -> (env'=1);
// message with old ip address arrives so count
[send1] error=0 & env=0 -> (k'=min(k+1,K));
// time passgae so update relevant clocks
[time] error=0 & env=0 & k=0 -> true;
[time] error=0 & env=0 & k=1 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1));
[time] error=0 & env=0 & k=2 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1));
[time] error=0 & env=0 & k=3 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1)) & (c3'=min(c3+1,M+1));
[time] error=0 & env=0 & k=4 & min(c1,c2,c3,c4)<M -> (c1'=min(c1+1,M+1)) & (c2'=min(c2+1,M+1)) & (c3'=min(c3+1,M+1)) & (c4'=min(c4+1,M+1));
// all clocks reached their bound so an error
[time] error=0 & env=0 & min(c1,c2,c3,c4)=M -> (error'=1);
// send a reply (then done)
[rec1] error=0 & env=0 & k>0 & min(c1,c2,c3,c4)<=M -> (env'=1);
// finished so any action can be performed
[time] error=1 | env=1 -> true;
[send1] error=1 | env=1 -> true;
[send2] error=1 | env=1 -> true;
[send2] error=1 | env=1 -> true;
[rec1] error=1 | env=1 -> true;
endmodule
//-------------------------------------------------------------
// error automaton for the time bounded assumption
// host does not send configured signal within T seconds
module time_error
time_error : [0..1];
done : [0..1];
t : [0..T];
[time] t<T-1 & done=0 & time_error=0 -> (t'=t+1); // time passes and bound not reached
[time] t=T-1 & done=0 & time_error=0 -> (time_error'=1); // bound reached so error
[configured] time_error=0 -> (done'=1); // configured within the time bound
// when in error or done state can loop with either action
[configured] time_error=1 | done=1 -> true;
[time] time_error=1 | done=1 -> true;
endmodule

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examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb4_10_numerical.pctl
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multi(Pmax=? [ F time_error=1 ] , P>=0.993141[ G (error=0) ])

1
examples/multiobjective/mdp/zeroconf-tb/zeroconf-tb4_10_pareto.pctl
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multi(Pmax=? [ F time_error=1 ] , Pmax=? [ G (error=0) ])

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