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Added PRISM files for all of our examples. Added missing reward models. Added result files that indicate the results of PRISM on our examples.
tempestpy_adaptions
Added PRISM files for all of our examples. Added missing reward models. Added result files that indicate the results of PRISM on our examples.
tempestpy_adaptions
dehnert
12 years ago
24 changed files with 1356 additions and 0 deletions
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3examples/dtmc/crowds/crowds.pctl
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19examples/dtmc/crowds/crowds.res
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80examples/dtmc/crowds/crowds10_5.pm
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95examples/dtmc/crowds/crowds15_5.pm
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110examples/dtmc/crowds/crowds20_5.pm
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65examples/dtmc/crowds/crowds5_5.pm
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4examples/dtmc/die/die.pctl
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31examples/dtmc/die/die.pm
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4examples/dtmc/die/die.res
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3examples/dtmc/synchronous_leader/leader.pctl
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14examples/dtmc/synchronous_leader/leader.res
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85examples/dtmc/synchronous_leader/leader3_5.pm
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89examples/dtmc/synchronous_leader/leader4_8.pm
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90examples/dtmc/synchronous_leader/leader5_8.pm
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91examples/dtmc/synchronous_leader/leader6_8.pm
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8examples/mdp/asynchronous_leader/leader.pctl
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49examples/mdp/asynchronous_leader/leader.res
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96examples/mdp/asynchronous_leader/leader3.nm
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97examples/mdp/asynchronous_leader/leader4.nm
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98examples/mdp/asynchronous_leader/leader5.nm
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99examples/mdp/asynchronous_leader/leader6.nm
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100examples/mdp/asynchronous_leader/leader7.nm
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13examples/mdp/two_dice/two_dice.pctl
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13examples/mdp/two_dice/two_dice.res
@ -0,0 +1,3 @@ |
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P=? [ F "observe0Greater1" ] |
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P=? [ F "observeIGreater1" ] |
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P=? [ F "observeOnlyTrueSender" ] |
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@ -0,0 +1,19 @@ |
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// 5/5 |
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P=? [ F "observe0Greater1" ] // 0.3328777473921436 |
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P=? [ F "observeIGreater1" ] // 0.15221847380560186 |
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P=? [ F "observeOnlyTrueSender" ] // 0.3215351607995943 |
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|
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// 10/5 |
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P=? [ F "observe0Greater1" ] // 0.26345583706046355 |
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P=? [ F "observeIGreater1" ] // 0.09236405558901994 |
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P=? [ F "observeOnlyTrueSender" ] // 0.25849872034453947 |
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// 15/5 |
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P=? [ F "observe0Greater1" ] // 0.2408422942249347 |
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P=? [ F "observeIGreater1" ] // 0.0655686905854717 |
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P=? [ F "observeOnlyTrueSender" ] // 0.2377298605519743 |
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|
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// 20/5 |
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P=? [ F "observe0Greater1" ] // 0.22967858575985317 |
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P=? [ F "observeIGreater1" ] // 0.05073192927314383 |
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P=? [ F "observeOnlyTrueSender" ] // 0.22742031678667812 |
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@ -0,0 +1,80 @@ |
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dtmc |
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|
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// probability of forwarding |
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const double PF = 0.8; |
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const double notPF = .2; // must be 1-PF |
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// probability that a crowd member is bad |
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const double badC = .167; |
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// probability that a crowd member is good |
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const double goodC = 0.833; |
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// Total number of protocol runs to analyze |
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const int TotalRuns = 5; |
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// size of the crowd |
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const int CrowdSize = 10; |
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module crowds |
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// protocol phase |
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phase: [0..4] init 0; |
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// crowd member good (or bad) |
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good: bool init false; |
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// number of protocol runs |
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runCount: [0..TotalRuns] init 0; |
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// observe_i is the number of times the attacker observed crowd member i |
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observe0: [0..TotalRuns] init 0; |
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observe1: [0..TotalRuns] init 0; |
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observe2: [0..TotalRuns] init 0; |
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observe3: [0..TotalRuns] init 0; |
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observe4: [0..TotalRuns] init 0; |
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observe5: [0..TotalRuns] init 0; |
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observe6: [0..TotalRuns] init 0; |
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observe7: [0..TotalRuns] init 0; |
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observe8: [0..TotalRuns] init 0; |
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observe9: [0..TotalRuns] init 0; |
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// the last seen crowd member |
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lastSeen: [0..CrowdSize - 1] init 0; |
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// get the protocol started |
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[] phase=0 & runCount<TotalRuns -> (phase'=1) & (runCount'=runCount+1) & (lastSeen'=0); |
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// decide whether crowd member is good or bad according to given probabilities |
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[] phase=1 -> goodC : (phase'=2) & (good'=true) + badC : (phase'=2) & (good'=false); |
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// if the current member is a good member, update the last seen index (chosen uniformly) |
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[] phase=2 & good -> 1/10 : (lastSeen'=0) & (phase'=3) + 1/10 : (lastSeen'=1) & (phase'=3) + 1/10 : (lastSeen'=2) & (phase'=3) + 1/10 : (lastSeen'=3) & (phase'=3) + 1/10 : (lastSeen'=4) & (phase'=3) + 1/10 : (lastSeen'=5) & (phase'=3) + 1/10 : (lastSeen'=6) & (phase'=3) + 1/10 : (lastSeen'=7) & (phase'=3) + 1/10 : (lastSeen'=8) & (phase'=3) + 1/10 : (lastSeen'=9) & (phase'=3); |
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// if the current member is a bad member, record the most recently seen index |
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[] phase=2 & !good & lastSeen=0 & observe0 < TotalRuns -> (observe0'=observe0+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=1 & observe1 < TotalRuns -> (observe1'=observe1+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=2 & observe2 < TotalRuns -> (observe2'=observe2+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=3 & observe3 < TotalRuns -> (observe3'=observe3+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=4 & observe4 < TotalRuns -> (observe4'=observe4+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=5 & observe5 < TotalRuns -> (observe5'=observe5+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=6 & observe6 < TotalRuns -> (observe6'=observe6+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=7 & observe7 < TotalRuns -> (observe7'=observe7+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=8 & observe8 < TotalRuns -> (observe8'=observe8+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=9 & observe9 < TotalRuns -> (observe9'=observe9+1) & (phase'=4); |
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// good crowd members forward with probability PF and deliver otherwise |
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[] phase=3 -> PF : (phase'=1) + notPF : (phase'=4); |
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// deliver the message and start over |
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[] phase=4 -> (phase'=0); |
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endmodule |
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label "observe0Greater1" = observe0 > 1; |
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label "observeIGreater1" = observe1 > 1 | observe2 > 1 | observe3 > 1 | observe4 > 1 | observe5 > 1 | observe6 > 1 | observe7 > 1 | observe8 > 1 | observe9 > 1; |
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label "observeOnlyTrueSender" = observe0 > 1 & observe1 <= 1 & observe2 <= 1 & observe3 <= 1 & observe4 <= 1 & observe5 <= 1 & observe6 <= 1 & observe7 <= 1 & observe8 <= 1 & observe9 <= 1; |
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@ -0,0 +1,95 @@ |
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dtmc |
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// probability of forwarding |
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const double PF = 0.8; |
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const double notPF = .2; // must be 1-PF |
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// probability that a crowd member is bad |
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const double badC = .167; |
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// probability that a crowd member is good |
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const double goodC = 0.833; |
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// Total number of protocol runs to analyze |
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const int TotalRuns = 5; |
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// size of the crowd |
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const int CrowdSize = 15; |
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module crowds |
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// protocol phase |
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phase: [0..4] init 0; |
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// crowd member good (or bad) |
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good: bool init false; |
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// number of protocol runs |
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runCount: [0..TotalRuns] init 0; |
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// observe_i is the number of times the attacker observed crowd member i |
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observe0: [0..TotalRuns] init 0; |
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observe1: [0..TotalRuns] init 0; |
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observe2: [0..TotalRuns] init 0; |
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observe3: [0..TotalRuns] init 0; |
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observe4: [0..TotalRuns] init 0; |
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observe5: [0..TotalRuns] init 0; |
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observe6: [0..TotalRuns] init 0; |
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observe7: [0..TotalRuns] init 0; |
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observe8: [0..TotalRuns] init 0; |
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observe9: [0..TotalRuns] init 0; |
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observe10: [0..TotalRuns] init 0; |
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observe11: [0..TotalRuns] init 0; |
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observe12: [0..TotalRuns] init 0; |
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observe13: [0..TotalRuns] init 0; |
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observe14: [0..TotalRuns] init 0; |
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// the last seen crowd member |
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lastSeen: [0..CrowdSize - 1] init 0; |
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// get the protocol started |
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[] phase=0 & runCount<TotalRuns -> (phase'=1) & (runCount'=runCount+1) & (lastSeen'=0); |
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// decide whether crowd member is good or bad according to given probabilities |
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[] phase=1 -> goodC : (phase'=2) & (good'=true) + badC : (phase'=2) & (good'=false); |
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// if the current member is a good member, update the last seen index (chosen uniformly) |
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[] phase=2 & good -> 1/15 : (lastSeen'=0) & (phase'=3) + 1/15 : (lastSeen'=1) & (phase'=3) + 1/15 : (lastSeen'=2) & (phase'=3) + 1/15 : (lastSeen'=3) & (phase'=3) + 1/15 : (lastSeen'=4) & (phase'=3) + 1/15 : (lastSeen'=5) & (phase'=3) + 1/15 : (lastSeen'=6) & (phase'=3) + 1/15 : (lastSeen'=7) & (phase'=3) + 1/15 : (lastSeen'=8) & (phase'=3) + 1/15 : (lastSeen'=9) & (phase'=3) + 1/15 : (lastSeen'=10) & (phase'=3) + 1/15 : (lastSeen'=11) & (phase'=3) + 1/15 : (lastSeen'=12) & (phase'=3) + 1/15 : (lastSeen'=13) & (phase'=3) + 1/15 : (lastSeen'=14) & (phase'=3); |
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// if the current member is a bad member, record the most recently seen index |
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[] phase=2 & !good & lastSeen=0 & observe0 < TotalRuns -> (observe0'=observe0+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=1 & observe1 < TotalRuns -> (observe1'=observe1+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=2 & observe2 < TotalRuns -> (observe2'=observe2+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=3 & observe3 < TotalRuns -> (observe3'=observe3+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=4 & observe4 < TotalRuns -> (observe4'=observe4+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=5 & observe5 < TotalRuns -> (observe5'=observe5+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=6 & observe6 < TotalRuns -> (observe6'=observe6+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=7 & observe7 < TotalRuns -> (observe7'=observe7+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=8 & observe8 < TotalRuns -> (observe8'=observe8+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=9 & observe9 < TotalRuns -> (observe9'=observe9+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=10 & observe10 < TotalRuns -> (observe10'=observe10+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=11 & observe11 < TotalRuns -> (observe11'=observe11+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=12 & observe12 < TotalRuns -> (observe12'=observe12+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=13 & observe13 < TotalRuns -> (observe13'=observe13+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=14 & observe14 < TotalRuns -> (observe14'=observe14+1) & (phase'=4); |
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// good crowd members forward with probability PF and deliver otherwise |
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[] phase=3 -> PF : (phase'=1) + notPF : (phase'=4); |
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// deliver the message and start over |
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[] phase=4 -> (phase'=0); |
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endmodule |
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label "observe0Greater1" = observe0 > 1; |
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label "observeIGreater1" = observe1 > 1 | observe2 > 1 | observe3 > 1 | observe4 > 1 | observe5 > 1 | observe6 > 1 | observe7 > 1 | observe8 > 1 | observe9 > 1 | observe10 > 1 | observe11 > 1 | observe12 > 1 | observe13 > 1 | observe14 > 1; |
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label "observeOnlyTrueSender" = observe0 > 1 & observe1 <= 1 & observe2 <= 1 & observe3 <= 1 & observe4 <= 1 & observe5 <= 1 & observe6 <= 1 & observe7 <= 1 & observe8 <= 1 & observe9 <= 1 & observe10 <= 1 & observe11 <= 1 & observe12 <= 1 & observe13 <= 1 & observe14 <= 1; |
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@ -0,0 +1,110 @@ |
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dtmc |
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// probability of forwarding |
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const double PF = 0.8; |
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const double notPF = .2; // must be 1-PF |
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// probability that a crowd member is bad |
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const double badC = .167; |
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// probability that a crowd member is good |
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const double goodC = 0.833; |
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// Total number of protocol runs to analyze |
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const int TotalRuns = 5; |
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// size of the crowd |
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const int CrowdSize = 20; |
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module crowds |
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// protocol phase |
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phase: [0..4] init 0; |
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// crowd member good (or bad) |
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good: bool init false; |
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// number of protocol runs |
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runCount: [0..TotalRuns] init 0; |
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// observe_i is the number of times the attacker observed crowd member i |
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observe0: [0..TotalRuns] init 0; |
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observe1: [0..TotalRuns] init 0; |
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observe2: [0..TotalRuns] init 0; |
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observe3: [0..TotalRuns] init 0; |
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observe4: [0..TotalRuns] init 0; |
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observe5: [0..TotalRuns] init 0; |
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observe6: [0..TotalRuns] init 0; |
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observe7: [0..TotalRuns] init 0; |
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observe8: [0..TotalRuns] init 0; |
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observe9: [0..TotalRuns] init 0; |
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observe10: [0..TotalRuns] init 0; |
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observe11: [0..TotalRuns] init 0; |
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observe12: [0..TotalRuns] init 0; |
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observe13: [0..TotalRuns] init 0; |
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observe14: [0..TotalRuns] init 0; |
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observe15: [0..TotalRuns] init 0; |
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observe16: [0..TotalRuns] init 0; |
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observe17: [0..TotalRuns] init 0; |
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observe18: [0..TotalRuns] init 0; |
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observe19: [0..TotalRuns] init 0; |
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// the last seen crowd member |
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lastSeen: [0..CrowdSize - 1] init 0; |
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// get the protocol started |
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[] phase=0 & runCount<TotalRuns -> (phase'=1) & (runCount'=runCount+1) & (lastSeen'=0); |
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// decide whether crowd member is good or bad according to given probabilities |
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[] phase=1 -> goodC : (phase'=2) & (good'=true) + badC : (phase'=2) & (good'=false); |
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// if the current member is a good member, update the last seen index (chosen uniformly) |
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[] phase=2 & good -> 1/20 : (lastSeen'=0) & (phase'=3) + 1/20 : (lastSeen'=1) & (phase'=3) + 1/20 : (lastSeen'=2) & (phase'=3) + 1/20 : (lastSeen'=3) & (phase'=3) + 1/20 : (lastSeen'=4) & (phase'=3) + 1/20 : (lastSeen'=5) & (phase'=3) + 1/20 : (lastSeen'=6) & (phase'=3) + 1/20 : (lastSeen'=7) & (phase'=3) + 1/20 : (lastSeen'=8) & (phase'=3) + 1/20 : (lastSeen'=9) & (phase'=3) + 1/20 : (lastSeen'=10) & (phase'=3) + 1/20 : (lastSeen'=11) & (phase'=3) + 1/20 : (lastSeen'=12) & (phase'=3) + 1/20 : (lastSeen'=13) & (phase'=3) + 1/20 : (lastSeen'=14) & (phase'=3) + 1/20 : (lastSeen'=15) & (phase'=3) + 1/20 : (lastSeen'=16) & (phase'=3) + 1/20 : (lastSeen'=17) & (phase'=3) + 1/20 : (lastSeen'=18) & (phase'=3) + 1/20 : (lastSeen'=19) & (phase'=3); |
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// if the current member is a bad member, record the most recently seen index |
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[] phase=2 & !good & lastSeen=0 & observe0 < TotalRuns -> (observe0'=observe0+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=1 & observe1 < TotalRuns -> (observe1'=observe1+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=2 & observe2 < TotalRuns -> (observe2'=observe2+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=3 & observe3 < TotalRuns -> (observe3'=observe3+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=4 & observe4 < TotalRuns -> (observe4'=observe4+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=5 & observe5 < TotalRuns -> (observe5'=observe5+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=6 & observe6 < TotalRuns -> (observe6'=observe6+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=7 & observe7 < TotalRuns -> (observe7'=observe7+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=8 & observe8 < TotalRuns -> (observe8'=observe8+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=9 & observe9 < TotalRuns -> (observe9'=observe9+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=10 & observe10 < TotalRuns -> (observe10'=observe10+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=11 & observe11 < TotalRuns -> (observe11'=observe11+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=12 & observe12 < TotalRuns -> (observe12'=observe12+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=13 & observe13 < TotalRuns -> (observe13'=observe13+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=14 & observe14 < TotalRuns -> (observe14'=observe14+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=15 & observe15 < TotalRuns -> (observe15'=observe15+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=16 & observe16 < TotalRuns -> (observe16'=observe16+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=17 & observe17 < TotalRuns -> (observe17'=observe17+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=18 & observe18 < TotalRuns -> (observe18'=observe18+1) & (phase'=4); |
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[] phase=2 & !good & lastSeen=19 & observe19 < TotalRuns -> (observe19'=observe19+1) & (phase'=4); |
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// good crowd members forward with probability PF and deliver otherwise |
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[] phase=3 -> PF : (phase'=1) + notPF : (phase'=4); |
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// deliver the message and start over |
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[] phase=4 -> (phase'=0); |
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endmodule |
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|
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label "observe0Greater1" = observe0 > 1; |
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label "observeIGreater1" = observe1 > 1 | observe2 > 1 | observe3 > 1 | observe4 > 1 | observe5 > 1 | observe6 > 1 | observe7 > 1 | observe8 > 1 | observe9 > 1 | observe10 > 1 | observe11 > 1 | observe12 > 1 | observe13 > 1 | observe14 > 1 | observe15 > 1 | observe16 > 1 | observe17 > 1 | observe18 > 1 | observe19 > 1; |
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label "observeOnlyTrueSender" = observe0 > 1 & observe1 <= 1 & observe2 <= 1 & observe3 <= 1 & observe4 <= 1 & observe5 <= 1 & observe6 <= 1 & observe7 <= 1 & observe8 <= 1 & observe9 <= 1 & observe10 <= 1 & observe11 <= 1 & observe12 <= 1 & observe13 <= 1 & observe14 <= 1 & observe15 <= 1 & observe16 <= 1 & observe17 <= 1 & observe18 <= 1 & observe19 <= 1; |
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@ -0,0 +1,65 @@ |
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dtmc |
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|
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// probability of forwarding |
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const double PF = 0.8; |
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const double notPF = .2; // must be 1-PF |
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// probability that a crowd member is bad |
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const double badC = .167; |
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// probability that a crowd member is good |
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const double goodC = 0.833; |
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// Total number of protocol runs to analyze |
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const int TotalRuns = 5; |
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// size of the crowd |
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const int CrowdSize = 5; |
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|
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module crowds |
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// protocol phase |
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phase: [0..4] init 0; |
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|
|||
// crowd member good (or bad) |
|||
good: bool init false; |
|||
|
|||
// number of protocol runs |
|||
runCount: [0..TotalRuns] init 0; |
|||
|
|||
// observe_i is the number of times the attacker observed crowd member i |
|||
observe0: [0..TotalRuns] init 0; |
|||
|
|||
observe1: [0..TotalRuns] init 0; |
|||
|
|||
observe2: [0..TotalRuns] init 0; |
|||
|
|||
observe3: [0..TotalRuns] init 0; |
|||
|
|||
observe4: [0..TotalRuns] init 0; |
|||
|
|||
// the last seen crowd member |
|||
lastSeen: [0..CrowdSize - 1] init 0; |
|||
|
|||
// get the protocol started |
|||
[] phase=0 & runCount<TotalRuns -> (phase'=1) & (runCount'=runCount+1) & (lastSeen'=0); |
|||
|
|||
// decide whether crowd member is good or bad according to given probabilities |
|||
[] phase=1 -> goodC : (phase'=2) & (good'=true) + badC : (phase'=2) & (good'=false); |
|||
|
|||
// if the current member is a good member, update the last seen index (chosen uniformly) |
|||
[] phase=2 & good -> 1/5 : (lastSeen'=0) & (phase'=3) + 1/5 : (lastSeen'=1) & (phase'=3) + 1/5 : (lastSeen'=2) & (phase'=3) + 1/5 : (lastSeen'=3) & (phase'=3) + 1/5 : (lastSeen'=4) & (phase'=3); |
|||
|
|||
// if the current member is a bad member, record the most recently seen index |
|||
[] phase=2 & !good & lastSeen=0 & observe0 < TotalRuns -> (observe0'=observe0+1) & (phase'=4); |
|||
[] phase=2 & !good & lastSeen=1 & observe1 < TotalRuns -> (observe1'=observe1+1) & (phase'=4); |
|||
[] phase=2 & !good & lastSeen=2 & observe2 < TotalRuns -> (observe2'=observe2+1) & (phase'=4); |
|||
[] phase=2 & !good & lastSeen=3 & observe3 < TotalRuns -> (observe3'=observe3+1) & (phase'=4); |
|||
[] phase=2 & !good & lastSeen=4 & observe4 < TotalRuns -> (observe4'=observe4+1) & (phase'=4); |
|||
|
|||
// good crowd members forward with probability PF and deliver otherwise |
|||
[] phase=3 -> PF : (phase'=1) + notPF : (phase'=4); |
|||
|
|||
// deliver the message and start over |
|||
[] phase=4 -> (phase'=0); |
|||
|
|||
endmodule |
|||
|
|||
label "observe0Greater1" = observe0 > 1; |
|||
label "observeIGreater1" = observe1 > 1 | observe2 > 1 | observe3 > 1 | observe4 > 1; |
|||
label "observeOnlyTrueSender" = observe0 > 1 & observe1 <= 1 & observe2 <= 1 & observe3 <= 1 & observe4 <= 1; |
|||
@ -0,0 +1,4 @@ |
|||
P=? [ F "one" ] |
|||
P=? [ F "two" ] |
|||
P=? [ F "three" ] |
|||
R=? [ F "done" ] |
|||
@ -0,0 +1,31 @@ |
|||
dtmc |
|||
|
|||
module die |
|||
|
|||
// local state |
|||
s : [0..7] init 0; |
|||
// value of the die |
|||
d : [0..6] init 0; |
|||
|
|||
[] s=0 -> 0.5 : (s'=1) + 0.5 : (s'=2); |
|||
[] s=1 -> 0.5 : (s'=3) + 0.5 : (s'=4); |
|||
[] s=2 -> 0.5 : (s'=5) + 0.5 : (s'=6); |
|||
[] s=3 -> 0.5 : (s'=1) + 0.5 : (s'=7) & (d'=1); |
|||
[] s=4 -> 0.5 : (s'=7) & (d'=2) + 0.5 : (s'=7) & (d'=3); |
|||
[] s=5 -> 0.5 : (s'=7) & (d'=4) + 0.5 : (s'=7) & (d'=5); |
|||
[] s=6 -> 0.5 : (s'=2) + 0.5 : (s'=7) & (d'=6); |
|||
[] s=7 -> (s'=7); |
|||
|
|||
endmodule |
|||
|
|||
rewards "coin_flips" |
|||
[] s<7 : 1; |
|||
endrewards |
|||
|
|||
label "one" = s=7&d=1; |
|||
label "two" = s=7&d=2; |
|||
label "three" = s=7&d=3; |
|||
label "four" = s=7&d=4; |
|||
label "five" = s=7&d=5; |
|||
label "six" = s=7&d=6; |
|||
label "done" = s=7; |
|||
@ -0,0 +1,4 @@ |
|||
P=? [ F "one" ] // 0.16666650772094727 |
|||
P=? [ F "two" ] // 0.16666650772094727 |
|||
P=? [ F "three" ] // 0.16666650772094727 |
|||
R=? [ F "done" ] // 3.6666650772094727 |
|||
@ -0,0 +1,3 @@ |
|||
P=? [ F "elected" ] |
|||
P=? [ F<=(4*(N+1)) "elected" ] |
|||
R=? [ F "elected" ] |
|||
@ -0,0 +1,14 @@ |
|||
// 3/5 |
|||
P=? [ F "elected" ] // 1.0 |
|||
P=? [ F<=(4*(N+1)) "elected" ] // 0.999997440000001 |
|||
R=? [ F "elected" ] // 1.0416666623999995 |
|||
|
|||
// 4/8 |
|||
P=? [ F "elected" ] // 1.0 |
|||
P=? [ F<=(4*(N+1)) "elected" ] // 0.9999965911265463 |
|||
R=? [ F "elected" ] // 1.0448979526072435 |
|||
|
|||
// 5/8 |
|||
P=? [ F "elected" ] // 1.0 |
|||
P=? [ F<=(4*(N+1)) "elected" ] // 0.9999999097195733 |
|||
R=? [ F "elected" ] // 1.0176397499602707 |
|||
@ -0,0 +1,85 @@ |
|||
// synchronous leader election protocol (itai & Rodeh) |
|||
// dxp/gxn 25/01/01 |
|||
|
|||
dtmc |
|||
|
|||
// CONSTANTS |
|||
const N = 3; // number of processes |
|||
const K = 5; // range of probabilistic choice |
|||
|
|||
// counter module used to count the number of processes that have been read |
|||
// and to know when a process has decided |
|||
module counter |
|||
|
|||
// counter (c=i means process j reading process (i-1)+j next) |
|||
c : [1..N-1]; |
|||
|
|||
// reading |
|||
[read] c<N-1 -> (c'=c+1); |
|||
// finished reading |
|||
[read] c=N-1 -> (c'=c); |
|||
//decide |
|||
[done] u1|u2|u3 -> (c'=c); |
|||
// pick again reset counter |
|||
[retry] !(u1|u2|u3) -> (c'=1); |
|||
// loop (when finished to avoid deadlocks) |
|||
[loop] s1=3 -> (c'=c); |
|||
|
|||
endmodule |
|||
|
|||
// processes form a ring and suppose: |
|||
// process 1 reads process 2 |
|||
// process 2 reads process 3 |
|||
// process 3 reads process 1 |
|||
module process1 |
|||
|
|||
// local state |
|||
s1 : [0..3]; |
|||
// s1=0 make random choice |
|||
// s1=1 reading |
|||
// s1=2 deciding |
|||
// s1=3 finished |
|||
|
|||
// has a unique id so far (initially true) |
|||
u1 : bool; |
|||
|
|||
// value to be sent to next process in the ring (initially sets this to its own value) |
|||
v1 : [0..K-1]; |
|||
|
|||
// random choice |
|||
p1 : [0..K-1]; |
|||
|
|||
// pick value |
|||
[pick] s1=0 -> 1/K : (s1'=1) & (p1'=0) & (v1'=0) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=1) & (v1'=1) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=2) & (v1'=2) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=3) & (v1'=3) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=4) & (v1'=4) & (u1'=true); |
|||
// read |
|||
[read] s1=1 & u1 & c<N-1 -> (u1'=(p1!=v2)) & (v1'=v2); |
|||
[read] s1=1 & !u1 & c<N-1 -> (u1'=false) & (v1'=v2) & (p1'=0); |
|||
// read and move to decide |
|||
[read] s1=1 & u1 & c=N-1 -> (s1'=2) & (u1'=(p1!=v2)) & (v1'=0) & (p1'=0); |
|||
[read] s1=1 & !u1 & c=N-1 -> (s1'=2) & (u1'=false) & (v1'=0); |
|||
// deciding |
|||
// done |
|||
[done] s1=2 -> (s1'=3) & (u1'=false) & (v1'=0) & (p1'=0); |
|||
//retry |
|||
[retry] s1=2 -> (s1'=0) & (u1'=false) & (v1'=0) & (p1'=0); |
|||
// loop (when finished to avoid deadlocks) |
|||
[loop] s1=3 -> (s1'=3); |
|||
|
|||
endmodule |
|||
|
|||
// construct remaining processes through renaming |
|||
module process2 = process1 [ s1=s2,p1=p2,v1=v2,u1=u2,v2=v3 ] endmodule |
|||
module process3 = process1 [ s1=s3,p1=p3,v1=v3,u1=u3,v2=v1 ] endmodule |
|||
|
|||
// expected number of rounds |
|||
rewards "num_rounds" |
|||
[pick] true : 1; |
|||
endrewards |
|||
|
|||
// labels |
|||
label "elected" = s1=3&s2=3&s3=3; |
|||
|
|||
@ -0,0 +1,89 @@ |
|||
// synchronous leader election protocol (itai & Rodeh) |
|||
// dxp/gxn 25/01/01 |
|||
|
|||
dtmc |
|||
|
|||
// CONSTANTS |
|||
const N = 4; // number of processes |
|||
const K = 8; // range of probabilistic choice |
|||
|
|||
// counter module used to count the number of processes that have been read |
|||
// and to know when a process has decided |
|||
module counter |
|||
|
|||
// counter (c=i means process j reading process (i-1)+j next) |
|||
c : [1..N-1]; |
|||
|
|||
// reading |
|||
[read] c<N-1 -> (c'=c+1); |
|||
// finished reading |
|||
[read] c=N-1 -> (c'=c); |
|||
//decide |
|||
[done] u1|u2|u3|u4 -> (c'=c); |
|||
// pick again reset counter |
|||
[retry] !(u1|u2|u3|u4) -> (c'=1); |
|||
// loop (when finished to avoid deadlocks) |
|||
[loop] s1=3 -> (c'=c); |
|||
|
|||
endmodule |
|||
|
|||
// processes form a ring and suppose: |
|||
// process 1 reads process 2 |
|||
// process 2 reads process 3 |
|||
// process 3 reads process 1 |
|||
module process1 |
|||
|
|||
// local state |
|||
s1 : [0..3]; |
|||
// s1=0 make random choice |
|||
// s1=1 reading |
|||
// s1=2 deciding |
|||
// s1=3 finished |
|||
|
|||
// has a unique id so far (initially true) |
|||
u1 : bool; |
|||
|
|||
// value to be sent to next process in the ring (initially sets this to its own value) |
|||
v1 : [0..K-1]; |
|||
|
|||
// random choice |
|||
p1 : [0..K-1]; |
|||
|
|||
// pick value |
|||
[pick] s1=0 -> 1/K : (s1'=1) & (p1'=0) & (v1'=0) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=1) & (v1'=1) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=2) & (v1'=2) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=3) & (v1'=3) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=4) & (v1'=4) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=5) & (v1'=5) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=6) & (v1'=6) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=7) & (v1'=7) & (u1'=true); |
|||
// read |
|||
[read] s1=1 & u1 & c<N-1 -> (u1'=(p1!=v2)) & (v1'=v2); |
|||
[read] s1=1 & !u1 & c<N-1 -> (u1'=false) & (v1'=v2) & (p1'=0); |
|||
// read and move to decide |
|||
[read] s1=1 & u1 & c=N-1 -> (s1'=2) & (u1'=(p1!=v2)) & (v1'=0) & (p1'=0); |
|||
[read] s1=1 & !u1 & c=N-1 -> (s1'=2) & (u1'=false) & (v1'=0); |
|||
// deciding |
|||
// done |
|||
[done] s1=2 -> (s1'=3) & (u1'=false) & (v1'=0) & (p1'=0); |
|||
//retry |
|||
[retry] s1=2 -> (s1'=0) & (u1'=false) & (v1'=0) & (p1'=0); |
|||
// loop (when finished to avoid deadlocks) |
|||
[loop] s1=3 -> (s1'=3); |
|||
|
|||
endmodule |
|||
|
|||
// construct remaining processes through renaming |
|||
module process2 = process1 [ s1=s2,p1=p2,v1=v2,u1=u2,v2=v3 ] endmodule |
|||
module process3 = process1 [ s1=s3,p1=p3,v1=v3,u1=u3,v2=v4 ] endmodule |
|||
module process4 = process1 [ s1=s4,p1=p4,v1=v4,u1=u4,v2=v1 ] endmodule |
|||
|
|||
// expected number of rounds |
|||
rewards "num_rounds" |
|||
[pick] true : 1; |
|||
endrewards |
|||
|
|||
// labels |
|||
label "elected" = s1=3&s2=3&s3=3&s4=3; |
|||
|
|||
@ -0,0 +1,90 @@ |
|||
// synchronous leader election protocol (itai & Rodeh) |
|||
// dxp/gxn 25/01/01 |
|||
|
|||
dtmc |
|||
|
|||
// CONSTANTS |
|||
const N = 5; // number of processes |
|||
const K = 8; // range of probabilistic choice |
|||
|
|||
// counter module used to count the number of processes that have been read |
|||
// and to know when a process has decided |
|||
module counter |
|||
|
|||
// counter (c=i means process j reading process (i-1)+j next) |
|||
c : [1..N-1]; |
|||
|
|||
// reading |
|||
[read] c<N-1 -> (c'=c+1); |
|||
// finished reading |
|||
[read] c=N-1 -> (c'=c); |
|||
//decide |
|||
[done] u1|u2|u3|u4|u5 -> (c'=c); |
|||
// pick again reset counter |
|||
[retry] !(u1|u2|u3|u4|u5) -> (c'=1); |
|||
// loop (when finished to avoid deadlocks) |
|||
[loop] s1=3 -> (c'=c); |
|||
|
|||
endmodule |
|||
|
|||
// processes form a ring and suppose: |
|||
// process 1 reads process 2 |
|||
// process 2 reads process 3 |
|||
// process 3 reads process 1 |
|||
module process1 |
|||
|
|||
// local state |
|||
s1 : [0..3]; |
|||
// s1=0 make random choice |
|||
// s1=1 reading |
|||
// s1=2 deciding |
|||
// s1=3 finished |
|||
|
|||
// has a unique id so far (initially true) |
|||
u1 : bool; |
|||
|
|||
// value to be sent to next process in the ring (initially sets this to its own value) |
|||
v1 : [0..K-1]; |
|||
|
|||
// random choice |
|||
p1 : [0..K-1]; |
|||
|
|||
// pick value |
|||
[pick] s1=0 -> 1/K : (s1'=1) & (p1'=0) & (v1'=0) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=1) & (v1'=1) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=2) & (v1'=2) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=3) & (v1'=3) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=4) & (v1'=4) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=5) & (v1'=5) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=6) & (v1'=6) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=7) & (v1'=7) & (u1'=true); |
|||
// read |
|||
[read] s1=1 & u1 & c<N-1 -> (u1'=(p1!=v2)) & (v1'=v2); |
|||
[read] s1=1 & !u1 & c<N-1 -> (u1'=false) & (v1'=v2) & (p1'=0); |
|||
// read and move to decide |
|||
[read] s1=1 & u1 & c=N-1 -> (s1'=2) & (u1'=(p1!=v2)) & (v1'=0) & (p1'=0); |
|||
[read] s1=1 & !u1 & c=N-1 -> (s1'=2) & (u1'=false) & (v1'=0); |
|||
// deciding |
|||
// done |
|||
[done] s1=2 -> (s1'=3) & (u1'=false) & (v1'=0) & (p1'=0); |
|||
//retry |
|||
[retry] s1=2 -> (s1'=0) & (u1'=false) & (v1'=0) & (p1'=0); |
|||
// loop (when finished to avoid deadlocks) |
|||
[loop] s1=3 -> (s1'=3); |
|||
|
|||
endmodule |
|||
|
|||
// construct remaining processes through renaming |
|||
module process2 = process1 [ s1=s2,p1=p2,v1=v2,u1=u2,v2=v3 ] endmodule |
|||
module process3 = process1 [ s1=s3,p1=p3,v1=v3,u1=u3,v2=v4 ] endmodule |
|||
module process4 = process1 [ s1=s4,p1=p4,v1=v4,u1=u4,v2=v5 ] endmodule |
|||
module process5 = process1 [ s1=s5,p1=p5,v1=v5,u1=u5,v2=v1 ] endmodule |
|||
|
|||
// expected number of rounds |
|||
rewards "num_rounds" |
|||
[pick] true : 1; |
|||
endrewards |
|||
|
|||
// labels |
|||
label "elected" = s1=3&s2=3&s3=3&s4=3&s5=3; |
|||
|
|||
@ -0,0 +1,91 @@ |
|||
// synchronous leader election protocol (itai & Rodeh) |
|||
// dxp/gxn 25/01/01 |
|||
|
|||
dtmc |
|||
|
|||
// CONSTANTS |
|||
const N = 6; // number of processes |
|||
const K = 8; // range of probabilistic choice |
|||
|
|||
// counter module used to count the number of processes that have been read |
|||
// and to know when a process has decided |
|||
module counter |
|||
|
|||
// counter (c=i means process j reading process (i-1)+j next) |
|||
c : [1..N-1]; |
|||
|
|||
// reading |
|||
[read] c<N-1 -> (c'=c+1); |
|||
// finished reading |
|||
[read] c=N-1 -> (c'=c); |
|||
//decide |
|||
[done] u1|u2|u3|u4|u5|u6 -> (c'=c); |
|||
// pick again reset counter |
|||
[retry] !(u1|u2|u3|u4|u5|u6) -> (c'=1); |
|||
// loop (when finished to avoid deadlocks) |
|||
[loop] s1=3 -> (c'=c); |
|||
|
|||
endmodule |
|||
|
|||
// processes form a ring and suppose: |
|||
// process 1 reads process 2 |
|||
// process 2 reads process 3 |
|||
// process 3 reads process 1 |
|||
module process1 |
|||
|
|||
// local state |
|||
s1 : [0..3]; |
|||
// s1=0 make random choice |
|||
// s1=1 reading |
|||
// s1=2 deciding |
|||
// s1=3 finished |
|||
|
|||
// has a unique id so far (initially true) |
|||
u1 : bool; |
|||
|
|||
// value to be sent to next process in the ring (initially sets this to its own value) |
|||
v1 : [0..K-1]; |
|||
|
|||
// random choice |
|||
p1 : [0..K-1]; |
|||
|
|||
// pick value |
|||
[pick] s1=0 -> 1/K : (s1'=1) & (p1'=0) & (v1'=0) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=1) & (v1'=1) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=2) & (v1'=2) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=3) & (v1'=3) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=4) & (v1'=4) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=5) & (v1'=5) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=6) & (v1'=6) & (u1'=true) |
|||
+ 1/K : (s1'=1) & (p1'=7) & (v1'=7) & (u1'=true); |
|||
// read |
|||
[read] s1=1 & u1 & c<N-1 -> (u1'=(p1!=v2)) & (v1'=v2); |
|||
[read] s1=1 & !u1 & c<N-1 -> (u1'=false) & (v1'=v2) & (p1'=0); |
|||
// read and move to decide |
|||
[read] s1=1 & u1 & c=N-1 -> (s1'=2) & (u1'=(p1!=v2)) & (v1'=0) & (p1'=0); |
|||
[read] s1=1 & !u1 & c=N-1 -> (s1'=2) & (u1'=false) & (v1'=0); |
|||
// deciding |
|||
// done |
|||
[done] s1=2 -> (s1'=3) & (u1'=false) & (v1'=0) & (p1'=0); |
|||
//retry |
|||
[retry] s1=2 -> (s1'=0) & (u1'=false) & (v1'=0) & (p1'=0); |
|||
// loop (when finished to avoid deadlocks) |
|||
[loop] s1=3 -> (s1'=3); |
|||
|
|||
endmodule |
|||
|
|||
// construct remaining processes through renaming |
|||
module process2 = process1 [ s1=s2,p1=p2,v1=v2,u1=u2,v2=v3 ] endmodule |
|||
module process3 = process1 [ s1=s3,p1=p3,v1=v3,u1=u3,v2=v4 ] endmodule |
|||
module process4 = process1 [ s1=s4,p1=p4,v1=v4,u1=u4,v2=v5 ] endmodule |
|||
module process5 = process1 [ s1=s5,p1=p5,v1=v5,u1=u5,v2=v6 ] endmodule |
|||
module process6 = process1 [ s1=s6,p1=p6,v1=v6,u1=u6,v2=v1 ] endmodule |
|||
|
|||
// expected number of rounds |
|||
rewards "num_rounds" |
|||
[pick] true : 1; |
|||
endrewards |
|||
|
|||
// labels |
|||
label "elected" = s1=3&s2=3&s3=3&s4=3&s5=3&s6=3; |
|||
|
|||
@ -0,0 +1,8 @@ |
|||
Pmin=? [ F "elected" ] |
|||
|
|||
const int K = 25; |
|||
Pmin=? [ F<=K "elected" ] |
|||
Pmax=? [ F<=K "elected" ] |
|||
|
|||
Rmin=? [ F "elected" ] |
|||
Rmax=? [ F "elected" ] |
|||
@ -0,0 +1,49 @@ |
|||
// 3 |
|||
Pmin=? [ F "elected" ] // 1.0 |
|||
|
|||
const int K = 25; |
|||
Pmin=? [ F<=K "elected" ] // 0.5625 |
|||
Pmax=? [ F<=K "elected" ] // 0.5625 |
|||
|
|||
Rmin=? [ F "elected" ] // 3.3333212586585432 |
|||
Rmax=? [ F "elected" ] // 3.3333206579554826 |
|||
|
|||
// 4 |
|||
Pmin=? [ F "elected" ] // 1.0 |
|||
|
|||
const int K = 25; |
|||
Pmin=? [ F<=K "elected" ] // 0.0625 |
|||
Pmax=? [ F<=K "elected" ] // 0.0625 |
|||
|
|||
Rmin=? [ F "elected" ] // 4.2856896106114934 |
|||
Rmax=? [ F "elected" ] // 4.28569043544414 |
|||
|
|||
// 5 |
|||
Pmin=? [ F "elected" ] // 1.0 |
|||
|
|||
const int K = 25; |
|||
Pmin=? [ F<=K "elected" ] // 0.0 |
|||
Pmax=? [ F<=K "elected" ] // 0.0 |
|||
|
|||
Rmin=? [ F "elected" ] // 5.034886386278894 |
|||
Rmax=? [ F "elected" ] // 5.034881859133309 |
|||
|
|||
// 6 |
|||
Pmin=? [ F "elected" ] // 1.0 |
|||
|
|||
const int K = 25; |
|||
Pmin=? [ F<=K "elected" ] // 0.0 |
|||
Pmax=? [ F<=K "elected" ] // 0.0 |
|||
|
|||
Rmin=? [ F "elected" ] // 5.649720120334257 |
|||
Rmax=? [ F "elected" ] // 5.649719114527437 |
|||
|
|||
// 7 |
|||
Pmin=? [ F "elected" ] // 1.0 |
|||
|
|||
const int K = 25; |
|||
Pmin=? [ F<=K "elected" ] // 0.0 |
|||
Pmax=? [ F<=K "elected" ] // 0.0 |
|||
|
|||
Rmin=? [ F "elected" ] // 6.172433512043686 |
|||
Rmax=? [ F "elected" ] // 6.172434400085756 |
|||
@ -0,0 +1,96 @@ |
|||
// asynchronous leader election |
|||
// 4 processes |
|||
// gxn/dxp 29/01/01 |
|||
|
|||
mdp |
|||
|
|||
const N= 3; // number of processes |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
module process1 |
|||
|
|||
// COUNTER |
|||
c1 : [0..3-1]; |
|||
|
|||
// STATES |
|||
s1 : [0..4]; |
|||
// 0 make choice |
|||
// 1 have not received neighbours choice |
|||
// 2 active |
|||
// 3 inactive |
|||
// 4 leader |
|||
|
|||
// PREFERENCE |
|||
p1 : [0..1]; |
|||
|
|||
// VARIABLES FOR SENDING AND RECEIVING |
|||
receive1 : [0..2]; |
|||
// not received anything |
|||
// received choice |
|||
// received counter |
|||
sent1 : [0..2]; |
|||
// not send anything |
|||
// sent choice |
|||
// sent counter |
|||
|
|||
// pick value |
|||
[] (s1=0) -> 0.5 : (s1'=1) & (p1'=0) + 0.5 : (s1'=1) & (p1'=1); |
|||
|
|||
// send preference |
|||
[p12] (s1=1) & (sent1=0) -> (sent1'=1); |
|||
// receive preference |
|||
// stay active |
|||
[p31] (s1=1) & (receive1=0) & !( (p1=0) & (p3=1) ) -> (s1'=2) & (receive1'=1); |
|||
// become inactive |
|||
[p31] (s1=1) & (receive1=0) & (p1=0) & (p3=1) -> (s1'=3) & (receive1'=1); |
|||
|
|||
// send preference (can now reset preference) |
|||
[p12] (s1=2) & (sent1=0) -> (sent1'=1) & (p1'=0); |
|||
// send counter (already sent preference) |
|||
// not received counter yet |
|||
[c12] (s1=2) & (sent1=1) & (receive1=1) -> (sent1'=2); |
|||
// received counter (pick again) |
|||
[c12] (s1=2) & (sent1=1) & (receive1=2) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// receive counter and not sent yet (note in this case do not pass it on as will send own counter) |
|||
[c31] (s1=2) & (receive1=1) & (sent1<2) -> (receive1'=2); |
|||
// receive counter and sent counter |
|||
// only active process (decide) |
|||
[c31] (s1=2) & (receive1=1) & (sent1=2) & (c3=N-1) -> (s1'=4) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
// other active process (pick again) |
|||
[c31] (s1=2) & (receive1=1) & (sent1=2) & (c3<N-1) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// send preference (must have received preference) and can now reset |
|||
[p12] (s1=3) & (receive1>0) & (sent1=0) -> (sent1'=1) & (p1'=0); |
|||
// send counter (must have received counter first) and can now reset |
|||
[c12] (s1=3) & (receive1=2) & (sent1=1) -> (s1'=3) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// receive preference |
|||
[p31] (s1=3) & (receive1=0) -> (p1'=p3) & (receive1'=1); |
|||
// receive counter |
|||
[c31] (s1=3) & (receive1=1) & (c3<N-1) -> (c1'=c3+1) & (receive1'=2); |
|||
|
|||
// done |
|||
[done] (s1=4) -> (s1'=s1); |
|||
// add loop for processes who are inactive |
|||
[done] (s1=3) -> (s1'=s1); |
|||
|
|||
endmodule |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// construct further stations through renaming |
|||
module process2=process1[s1=s2,p1=p2,c1=c2,sent1=sent2,receive1=receive2,p12=p23,p31=p12,c12=c23,c31=c12,p3=p1,c3=c1] endmodule |
|||
module process3=process1[s1=s3,p1=p3,c1=c3,sent1=sent3,receive1=receive3,p12=p31,p31=p23,c12=c31,c31=c23,p3=p2,c3=c2] endmodule |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// reward - expected number of rounds (equals the number of times a process receives a counter) |
|||
rewards |
|||
[c12] true : 1; |
|||
endrewards |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
formula leaders = (s1=4?1:0)+(s2=4?1:0)+(s3=4?1:0); |
|||
label "elected" = s1=4|s2=4|s3=4; |
|||
|
|||
@ -0,0 +1,97 @@ |
|||
// asynchronous leader election |
|||
// 4 processes |
|||
// gxn/dxp 29/01/01 |
|||
|
|||
mdp |
|||
|
|||
const N= 4; // number of processes |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
module process1 |
|||
|
|||
// COUNTER |
|||
c1 : [0..4-1]; |
|||
|
|||
// STATES |
|||
s1 : [0..4]; |
|||
// 0 make choice |
|||
// 1 have not received neighbours choice |
|||
// 2 active |
|||
// 3 inactive |
|||
// 4 leader |
|||
|
|||
// PREFERENCE |
|||
p1 : [0..1]; |
|||
|
|||
// VARIABLES FOR SENDING AND RECEIVING |
|||
receive1 : [0..2]; |
|||
// not received anything |
|||
// received choice |
|||
// received counter |
|||
sent1 : [0..2]; |
|||
// not send anything |
|||
// sent choice |
|||
// sent counter |
|||
|
|||
// pick value |
|||
[] (s1=0) -> 0.5 : (s1'=1) & (p1'=0) + 0.5 : (s1'=1) & (p1'=1); |
|||
|
|||
// send preference |
|||
[p12] (s1=1) & (sent1=0) -> (sent1'=1); |
|||
// receive preference |
|||
// stay active |
|||
[p41] (s1=1) & (receive1=0) & !( (p1=0) & (p4=1) ) -> (s1'=2) & (receive1'=1); |
|||
// become inactive |
|||
[p41] (s1=1) & (receive1=0) & (p1=0) & (p4=1) -> (s1'=3) & (receive1'=1); |
|||
|
|||
// send preference (can now reset preference) |
|||
[p12] (s1=2) & (sent1=0) -> (sent1'=1) & (p1'=0); |
|||
// send counter (already sent preference) |
|||
// not received counter yet |
|||
[c12] (s1=2) & (sent1=1) & (receive1=1) -> (sent1'=2); |
|||
// received counter (pick again) |
|||
[c12] (s1=2) & (sent1=1) & (receive1=2) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// receive counter and not sent yet (note in this case do not pass it on as will send own counter) |
|||
[c41] (s1=2) & (receive1=1) & (sent1<2) -> (receive1'=2); |
|||
// receive counter and sent counter |
|||
// only active process (decide) |
|||
[c41] (s1=2) & (receive1=1) & (sent1=2) & (c4=N-1) -> (s1'=4) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
// other active process (pick again) |
|||
[c41] (s1=2) & (receive1=1) & (sent1=2) & (c4<N-1) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// send preference (must have received preference) and can now reset |
|||
[p12] (s1=3) & (receive1>0) & (sent1=0) -> (sent1'=1) & (p1'=0); |
|||
// send counter (must have received counter first) and can now reset |
|||
[c12] (s1=3) & (receive1=2) & (sent1=1) -> (s1'=3) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// receive preference |
|||
[p41] (s1=3) & (receive1=0) -> (p1'=p4) & (receive1'=1); |
|||
// receive counter |
|||
[c41] (s1=3) & (receive1=1) & (c4<N-1) -> (c1'=c4+1) & (receive1'=2); |
|||
|
|||
// done |
|||
[done] (s1=4) -> (s1'=s1); |
|||
// add loop for processes who are inactive |
|||
[done] (s1=3) -> (s1'=s1); |
|||
|
|||
endmodule |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// construct further stations through renaming |
|||
module process2=process1[s1=s2,p1=p2,c1=c2,sent1=sent2,receive1=receive2,p12=p23,p41=p12,c12=c23,c41=c12,p4=p1,c4=c1] endmodule |
|||
module process3=process1[s1=s3,p1=p3,c1=c3,sent1=sent3,receive1=receive3,p12=p34,p41=p23,c12=c34,c41=c23,p4=p2,c4=c2] endmodule |
|||
module process4=process1[s1=s4,p1=p4,c1=c4,sent1=sent4,receive1=receive4,p12=p41,p41=p34,c12=c41,c41=c34,p4=p3,c4=c3] endmodule |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// reward - expected number of rounds (equals the number of times a process receives a counter) |
|||
rewards |
|||
[c12] true : 1; |
|||
endrewards |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
formula leaders = (s1=4?1:0)+(s2=4?1:0)+(s3=4?1:0)+(s4=4?1:0); |
|||
label "elected" = s1=4|s2=4|s3=4|s4=4; |
|||
|
|||
@ -0,0 +1,98 @@ |
|||
// asynchronous leader election |
|||
// 4 processes |
|||
// gxn/dxp 29/01/01 |
|||
|
|||
mdp |
|||
|
|||
const N= 5; // number of processes |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
module process1 |
|||
|
|||
// COUNTER |
|||
c1 : [0..5-1]; |
|||
|
|||
// STATES |
|||
s1 : [0..4]; |
|||
// 0 make choice |
|||
// 1 have not received neighbours choice |
|||
// 2 active |
|||
// 3 inactive |
|||
// 4 leader |
|||
|
|||
// PREFERENCE |
|||
p1 : [0..1]; |
|||
|
|||
// VARIABLES FOR SENDING AND RECEIVING |
|||
receive1 : [0..2]; |
|||
// not received anything |
|||
// received choice |
|||
// received counter |
|||
sent1 : [0..2]; |
|||
// not send anything |
|||
// sent choice |
|||
// sent counter |
|||
|
|||
// pick value |
|||
[] (s1=0) -> 0.5 : (s1'=1) & (p1'=0) + 0.5 : (s1'=1) & (p1'=1); |
|||
|
|||
// send preference |
|||
[p12] (s1=1) & (sent1=0) -> (sent1'=1); |
|||
// receive preference |
|||
// stay active |
|||
[p51] (s1=1) & (receive1=0) & !( (p1=0) & (p5=1) ) -> (s1'=2) & (receive1'=1); |
|||
// become inactive |
|||
[p51] (s1=1) & (receive1=0) & (p1=0) & (p5=1) -> (s1'=3) & (receive1'=1); |
|||
|
|||
// send preference (can now reset preference) |
|||
[p12] (s1=2) & (sent1=0) -> (sent1'=1) & (p1'=0); |
|||
// send counter (already sent preference) |
|||
// not received counter yet |
|||
[c12] (s1=2) & (sent1=1) & (receive1=1) -> (sent1'=2); |
|||
// received counter (pick again) |
|||
[c12] (s1=2) & (sent1=1) & (receive1=2) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// receive counter and not sent yet (note in this case do not pass it on as will send own counter) |
|||
[c51] (s1=2) & (receive1=1) & (sent1<2) -> (receive1'=2); |
|||
// receive counter and sent counter |
|||
// only active process (decide) |
|||
[c51] (s1=2) & (receive1=1) & (sent1=2) & (c5=N-1) -> (s1'=4) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
// other active process (pick again) |
|||
[c51] (s1=2) & (receive1=1) & (sent1=2) & (c5<N-1) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// send preference (must have received preference) and can now reset |
|||
[p12] (s1=3) & (receive1>0) & (sent1=0) -> (sent1'=1) & (p1'=0); |
|||
// send counter (must have received counter first) and can now reset |
|||
[c12] (s1=3) & (receive1=2) & (sent1=1) -> (s1'=3) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// receive preference |
|||
[p51] (s1=3) & (receive1=0) -> (p1'=p5) & (receive1'=1); |
|||
// receive counter |
|||
[c51] (s1=3) & (receive1=1) & (c5<N-1) -> (c1'=c5+1) & (receive1'=2); |
|||
|
|||
// done |
|||
[done] (s1=4) -> (s1'=s1); |
|||
// add loop for processes who are inactive |
|||
[done] (s1=3) -> (s1'=s1); |
|||
|
|||
endmodule |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// construct further stations through renaming |
|||
module process2=process1[s1=s2,p1=p2,c1=c2,sent1=sent2,receive1=receive2,p12=p23,p51=p12,c12=c23,c51=c12,p5=p1,c5=c1] endmodule |
|||
module process3=process1[s1=s3,p1=p3,c1=c3,sent1=sent3,receive1=receive3,p12=p34,p51=p23,c12=c34,c51=c23,p5=p2,c5=c2] endmodule |
|||
module process4=process1[s1=s4,p1=p4,c1=c4,sent1=sent4,receive1=receive4,p12=p45,p51=p34,c12=c45,c51=c34,p5=p3,c5=c3] endmodule |
|||
module process5=process1[s1=s5,p1=p5,c1=c5,sent1=sent5,receive1=receive5,p12=p51,p51=p45,c12=c51,c51=c45,p5=p4,c5=c4] endmodule |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// reward - expected number of rounds (equals the number of times a process receives a counter) |
|||
rewards |
|||
[c12] true : 1; |
|||
endrewards |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
formula leaders = (s1=4?1:0)+(s2=4?1:0)+(s3=4?1:0)+(s4=4?1:0)+(s5=4?1:0); |
|||
label "elected" = s1=4|s2=4|s3=4|s4=4|s5=4; |
|||
|
|||
@ -0,0 +1,99 @@ |
|||
// asynchronous leader election |
|||
// 4 processes |
|||
// gxn/dxp 29/01/01 |
|||
|
|||
mdp |
|||
|
|||
const N= 6; // number of processes |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
module process1 |
|||
|
|||
// COUNTER |
|||
c1 : [0..6-1]; |
|||
|
|||
// STATES |
|||
s1 : [0..4]; |
|||
// 0 make choice |
|||
// 1 have not received neighbours choice |
|||
// 2 active |
|||
// 3 inactive |
|||
// 4 leader |
|||
|
|||
// PREFERENCE |
|||
p1 : [0..1]; |
|||
|
|||
// VARIABLES FOR SENDING AND RECEIVING |
|||
receive1 : [0..2]; |
|||
// not received anything |
|||
// received choice |
|||
// received counter |
|||
sent1 : [0..2]; |
|||
// not send anything |
|||
// sent choice |
|||
// sent counter |
|||
|
|||
// pick value |
|||
[] (s1=0) -> 0.5 : (s1'=1) & (p1'=0) + 0.5 : (s1'=1) & (p1'=1); |
|||
|
|||
// send preference |
|||
[p12] (s1=1) & (sent1=0) -> (sent1'=1); |
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// receive preference |
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// stay active |
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[p61] (s1=1) & (receive1=0) & !( (p1=0) & (p6=1) ) -> (s1'=2) & (receive1'=1); |
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// become inactive |
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[p61] (s1=1) & (receive1=0) & (p1=0) & (p6=1) -> (s1'=3) & (receive1'=1); |
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|
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// send preference (can now reset preference) |
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[p12] (s1=2) & (sent1=0) -> (sent1'=1) & (p1'=0); |
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// send counter (already sent preference) |
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// not received counter yet |
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[c12] (s1=2) & (sent1=1) & (receive1=1) -> (sent1'=2); |
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// received counter (pick again) |
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[c12] (s1=2) & (sent1=1) & (receive1=2) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
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|
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// receive counter and not sent yet (note in this case do not pass it on as will send own counter) |
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[c61] (s1=2) & (receive1=1) & (sent1<2) -> (receive1'=2); |
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// receive counter and sent counter |
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// only active process (decide) |
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[c61] (s1=2) & (receive1=1) & (sent1=2) & (c6=N-1) -> (s1'=4) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
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// other active process (pick again) |
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[c61] (s1=2) & (receive1=1) & (sent1=2) & (c6<N-1) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
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|
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// send preference (must have received preference) and can now reset |
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[p12] (s1=3) & (receive1>0) & (sent1=0) -> (sent1'=1) & (p1'=0); |
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// send counter (must have received counter first) and can now reset |
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[c12] (s1=3) & (receive1=2) & (sent1=1) -> (s1'=3) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
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|
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// receive preference |
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[p61] (s1=3) & (receive1=0) -> (p1'=p6) & (receive1'=1); |
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// receive counter |
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[c61] (s1=3) & (receive1=1) & (c6<N-1) -> (c1'=c6+1) & (receive1'=2); |
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|
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// done |
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[done] (s1=4) -> (s1'=s1); |
|||
// add loop for processes who are inactive |
|||
[done] (s1=3) -> (s1'=s1); |
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|
|||
endmodule |
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|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
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|
|||
// construct further stations through renaming |
|||
module process2=process1[s1=s2,p1=p2,c1=c2,sent1=sent2,receive1=receive2,p12=p23,p61=p12,c12=c23,c61=c12,p6=p1,c6=c1] endmodule |
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module process3=process1[s1=s3,p1=p3,c1=c3,sent1=sent3,receive1=receive3,p12=p34,p61=p23,c12=c34,c61=c23,p6=p2,c6=c2] endmodule |
|||
module process4=process1[s1=s4,p1=p4,c1=c4,sent1=sent4,receive1=receive4,p12=p45,p61=p34,c12=c45,c61=c34,p6=p3,c6=c3] endmodule |
|||
module process5=process1[s1=s5,p1=p5,c1=c5,sent1=sent5,receive1=receive5,p12=p56,p61=p45,c12=c56,c61=c45,p6=p4,c6=c4] endmodule |
|||
module process6=process1[s1=s6,p1=p6,c1=c6,sent1=sent6,receive1=receive6,p12=p61,p61=p56,c12=c61,c61=c56,p6=p5,c6=c5] endmodule |
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|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// reward - expected number of rounds (equals the number of times a process receives a counter) |
|||
rewards |
|||
[c12] true : 1; |
|||
endrewards |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
formula leaders = (s1=4?1:0)+(s2=4?1:0)+(s3=4?1:0)+(s4=4?1:0)+(s5=4?1:0)+(s6=4?1:0); |
|||
label "elected" = s1=4|s2=4|s3=4|s4=4|s5=4|s6=4; |
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|
|||
@ -0,0 +1,100 @@ |
|||
// asynchronous leader election |
|||
// 4 processes |
|||
// gxn/dxp 29/01/01 |
|||
|
|||
mdp |
|||
|
|||
const N= 7; // number of processes |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
module process1 |
|||
|
|||
// COUNTER |
|||
c1 : [0..7-1]; |
|||
|
|||
// STATES |
|||
s1 : [0..4]; |
|||
// 0 make choice |
|||
// 1 have not received neighbours choice |
|||
// 2 active |
|||
// 3 inactive |
|||
// 4 leader |
|||
|
|||
// PREFERENCE |
|||
p1 : [0..1]; |
|||
|
|||
// VARIABLES FOR SENDING AND RECEIVING |
|||
receive1 : [0..2]; |
|||
// not received anything |
|||
// received choice |
|||
// received counter |
|||
sent1 : [0..2]; |
|||
// not send anything |
|||
// sent choice |
|||
// sent counter |
|||
|
|||
// pick value |
|||
[] (s1=0) -> 0.5 : (s1'=1) & (p1'=0) + 0.5 : (s1'=1) & (p1'=1); |
|||
|
|||
// send preference |
|||
[p12] (s1=1) & (sent1=0) -> (sent1'=1); |
|||
// receive preference |
|||
// stay active |
|||
[p71] (s1=1) & (receive1=0) & !( (p1=0) & (p7=1) ) -> (s1'=2) & (receive1'=1); |
|||
// become inactive |
|||
[p71] (s1=1) & (receive1=0) & (p1=0) & (p7=1) -> (s1'=3) & (receive1'=1); |
|||
|
|||
// send preference (can now reset preference) |
|||
[p12] (s1=2) & (sent1=0) -> (sent1'=1) & (p1'=0); |
|||
// send counter (already sent preference) |
|||
// not received counter yet |
|||
[c12] (s1=2) & (sent1=1) & (receive1=1) -> (sent1'=2); |
|||
// received counter (pick again) |
|||
[c12] (s1=2) & (sent1=1) & (receive1=2) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// receive counter and not sent yet (note in this case do not pass it on as will send own counter) |
|||
[c71] (s1=2) & (receive1=1) & (sent1<2) -> (receive1'=2); |
|||
// receive counter and sent counter |
|||
// only active process (decide) |
|||
[c71] (s1=2) & (receive1=1) & (sent1=2) & (c7=N-1) -> (s1'=4) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
// other active process (pick again) |
|||
[c71] (s1=2) & (receive1=1) & (sent1=2) & (c7<N-1) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// send preference (must have received preference) and can now reset |
|||
[p12] (s1=3) & (receive1>0) & (sent1=0) -> (sent1'=1) & (p1'=0); |
|||
// send counter (must have received counter first) and can now reset |
|||
[c12] (s1=3) & (receive1=2) & (sent1=1) -> (s1'=3) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); |
|||
|
|||
// receive preference |
|||
[p71] (s1=3) & (receive1=0) -> (p1'=p7) & (receive1'=1); |
|||
// receive counter |
|||
[c71] (s1=3) & (receive1=1) & (c7<N-1) -> (c1'=c7+1) & (receive1'=2); |
|||
|
|||
// done |
|||
[done] (s1=4) -> (s1'=s1); |
|||
// add loop for processes who are inactive |
|||
[done] (s1=3) -> (s1'=s1); |
|||
|
|||
endmodule |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// construct further stations through renaming |
|||
module process2=process1[s1=s2,p1=p2,c1=c2,sent1=sent2,receive1=receive2,p12=p23,p71=p12,c12=c23,c71=c12,p7=p1,c7=c1] endmodule |
|||
module process3=process1[s1=s3,p1=p3,c1=c3,sent1=sent3,receive1=receive3,p12=p34,p71=p23,c12=c34,c71=c23,p7=p2,c7=c2] endmodule |
|||
module process4=process1[s1=s4,p1=p4,c1=c4,sent1=sent4,receive1=receive4,p12=p45,p71=p34,c12=c45,c71=c34,p7=p3,c7=c3] endmodule |
|||
module process5=process1[s1=s5,p1=p5,c1=c5,sent1=sent5,receive1=receive5,p12=p56,p71=p45,c12=c56,c71=c45,p7=p4,c7=c4] endmodule |
|||
module process6=process1[s1=s6,p1=p6,c1=c6,sent1=sent6,receive1=receive6,p12=p67,p71=p56,c12=c67,c71=c56,p7=p5,c7=c5] endmodule |
|||
module process7=process1[s1=s7,p1=p7,c1=c7,sent1=sent7,receive1=receive7,p12=p71,p71=p67,c12=c71,c71=c67,p7=p6,c7=c6] endmodule |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
|
|||
// reward - expected number of rounds (equals the number of times a process receives a counter) |
|||
rewards |
|||
[c12] true : 1; |
|||
endrewards |
|||
|
|||
//---------------------------------------------------------------------------------------------------------------------------- |
|||
formula leaders = (s1=4?1:0)+(s2=4?1:0)+(s3=4?1:0)+(s4=4?1:0)+(s5=4?1:0)+(s6=4?1:0)+(s7=4?1:0); |
|||
label "elected" = s1=4|s2=4|s3=4|s4=4|s5=4|s6=4|s7=4; |
|||
|
|||
@ -0,0 +1,13 @@ |
|||
Pmin=? [ F "two" ] |
|||
Pmax=? [ F "two" ] |
|||
Pmin=? [ F "three" ] |
|||
Pmax=? [ F "three" ] |
|||
Pmin=? [ F "four" ] |
|||
Pmax=? [ F "four" ] |
|||
Pmin=? [ F "five" ] |
|||
Pmax=? [ F "five" ] |
|||
Pmin=? [ F "six" ] |
|||
Pmax=? [ F "six" ] |
|||
|
|||
Rmin=? [ F "done" ] |
|||
Rmax=? [ F "done" ] |
|||
@ -0,0 +1,13 @@ |
|||
Pmin=? [ F "two" ] // 0.027777761220932007 |
|||
Pmax=? [ F "two" ] // 0.027777761220932007 |
|||
Pmin=? [ F "three" ] // 0.055555522441864014 |
|||
Pmax=? [ F "three" ] // 0.055555522441864014 |
|||
Pmin=? [ F "four" ] // 0.08333328366279602 |
|||
Pmax=? [ F "four" ] // 0.08333328366279602 |
|||
Pmin=? [ F "five" ] // 0.11111104488372803 |
|||
Pmax=? [ F "five" ] // 0.11111104488372803 |
|||
Pmin=? [ F "six" ] // 0.13888880610466003 |
|||
Pmax=? [ F "six" ] // 0.13888880610466003 |
|||
|
|||
Rmin=? [ F "done" ] // 7.333329498767853 |
|||
Rmax=? [ F "done" ] // 7.333329498767853 |
|||
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