dehnert
10 years ago
23 changed files with 904 additions and 56 deletions
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175src/builder/DdPrismModelBuilder.cpp
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16src/builder/DdPrismModelBuilder.h
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6src/builder/ExplicitPrismModelBuilder.cpp
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2src/parser/PrismParser.cpp
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7src/storage/expressions/Expression.cpp
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8src/storage/expressions/Expression.h
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15src/storage/prism/Command.cpp
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9src/storage/prism/Command.h
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25src/storage/prism/Module.cpp
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8src/storage/prism/Module.h
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84src/storage/prism/Program.cpp
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20src/storage/prism/Program.h
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14src/storage/prism/RewardModel.cpp
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9src/storage/prism/RewardModel.h
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3src/utility/cli.h
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27test/functional/builder/DdPrismModelBuilderTest.cpp
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28test/functional/builder/ExplicitPrismModelBuilderTest.cpp
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60test/functional/builder/coin2-2.nm
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130test/functional/builder/csma2-2.nm
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170test/functional/builder/firewire3-0.5.nm
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91test/functional/builder/leader3.nm
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40test/functional/builder/two_dice.nm
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13wlan0_collide.nm
@ -0,0 +1,60 @@ |
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// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90] |
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// gxn/dxp 20/11/00 |
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mdp |
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|
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// constants |
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const int N=2; |
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const int K=2; |
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const int range = 2*(K+1)*N; |
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const int counter_init = (K+1)*N; |
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const int left = N; |
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const int right = 2*(K+1)*N - N; |
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|
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// shared coin |
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global counter : [0..range] init counter_init; |
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module process1 |
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// program counter |
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pc1 : [0..3]; |
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// 0 - flip |
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// 1 - write |
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// 2 - check |
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// 3 - finished |
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|
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// local coin |
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coin1 : [0..1]; |
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|
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// flip coin |
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[] (pc1=0) -> 0.5 : (coin1'=0) & (pc1'=1) + 0.5 : (coin1'=1) & (pc1'=1); |
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// write tails -1 (reset coin to add regularity) |
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[] (pc1=1) & (coin1=0) & (counter>0) -> 1 : (counter'=counter-1) & (pc1'=2) & (coin1'=0); |
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// write heads +1 (reset coin to add regularity) |
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[] (pc1=1) & (coin1=1) & (counter<range) -> 1 : (counter'=counter+1) & (pc1'=2) & (coin1'=0); |
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// check |
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// decide tails |
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[] (pc1=2) & (counter<=left) -> 1 : (pc1'=3) & (coin1'=0); |
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// decide heads |
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[] (pc1=2) & (counter>=right) -> 1 : (pc1'=3) & (coin1'=1); |
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// flip again |
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[] (pc1=2) & (counter>left) & (counter<right) -> 1 : (pc1'=0); |
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// loop (all loop together when done) |
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[done] (pc1=3) -> 1 : (pc1'=3); |
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endmodule |
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// construct remaining processes through renaming |
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module process2 = process1[pc1=pc2,coin1=coin2] endmodule |
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// labels |
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label "finished" = pc1=3 & pc2=3 ; |
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label "all_coins_equal_0" = coin1=0 & coin2=0 ; |
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label "all_coins_equal_1" = coin1=1 & coin2=1 ; |
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label "agree" = coin1=coin2 ; |
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// rewards |
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rewards "steps" |
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true : 1; |
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endrewards |
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@ -0,0 +1,130 @@ |
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// CSMA/CD protocol - probabilistic version of kronos model (3 stations) |
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// gxn/dxp 04/12/01 |
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mdp |
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// note made changes since cannot have strict inequalities |
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// in digital clocks approach and suppose a station only sends one message |
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|
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// simplified parameters scaled |
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const int sigma=1; // time for messages to propagate along the bus |
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const int lambda=30; // time to send a message |
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// actual parameters |
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const int N = 2; // number of processes |
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const int K = 2; // exponential backoff limit |
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const int slot = 2*sigma; // length of slot |
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// const int M = floor(pow(2, K))-1 ; // max number of slots to wait |
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const int M = 3 ; // max number of slots to wait |
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//const int lambda=782; |
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//const int sigma=26; |
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// formula min_backoff_after_success = min(s1=4?cd1:K+1,s2=4?cd2:K+1); |
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// formula min_collisions = min(cd1,cd2); |
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// formula max_collisions = max(cd1,cd2); |
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//---------------------------------------------------------------------------------------------------------------------------- |
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// the bus |
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module bus |
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b : [0..2]; |
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// b=0 - idle |
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// b=1 - active |
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// b=2 - collision |
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// clocks of bus |
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y1 : [0..sigma+1]; // time since first send (used find time until channel sensed busy) |
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y2 : [0..sigma+1]; // time since second send (used to find time until collision detected) |
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// a sender sends (ok - no other message being sent) |
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[send1] (b=0) -> (b'=1); |
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[send2] (b=0) -> (b'=1); |
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// a sender sends (bus busy - collision) |
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[send1] (b=1|b=2) & (y1<sigma) -> (b'=2); |
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[send2] (b=1|b=2) & (y1<sigma) -> (b'=2); |
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|
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// finish sending |
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[end1] (b=1) -> (b'=0) & (y1'=0); |
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[end2] (b=1) -> (b'=0) & (y1'=0); |
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// bus busy |
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[busy1] (b=1|b=2) & (y1>=sigma) -> (b'=b); |
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[busy2] (b=1|b=2) & (y1>=sigma) -> (b'=b); |
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// collision detected |
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[cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0); |
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// time passage |
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[time] (b=0) -> (y1'=0); // value of y1/y2 does not matter in state 0 |
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[time] (b=1) -> (y1'=min(y1+1,sigma+1)); // no invariant in state 1 |
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[time] (b=2) & (y2<sigma) -> (y1'=min(y1+1,sigma+1)) & (y2'=min(y2+1,sigma+1)); // invariant in state 2 (time until collision detected) |
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endmodule |
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//---------------------------------------------------------------------------------------------------------------------------- |
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// model of first sender |
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module station1 |
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// LOCAL STATE |
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s1 : [0..5]; |
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// s1=0 - initial state |
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// s1=1 - transmit |
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// s1=2 - collision (set backoff) |
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// s1=3 - wait (bus busy) |
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// s1=4 - successfully sent |
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// LOCAL CLOCK |
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x1 : [0..max(lambda,slot)]; |
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// BACKOFF COUNTER (number of slots to wait) |
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bc1 : [0..M]; |
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// COLLISION COUNTER |
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cd1 : [0..K]; |
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// start sending |
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[send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending |
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[busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff |
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// transmitting |
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[time] (s1=1) & (x1<lambda) -> (x1'=min(x1+1,lambda)); // let time pass |
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[end1] (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished |
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[cd] (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected (increment backoff counter) |
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[cd] !(s1=1) -> (s1'=s1); // add loop for collision detection when not important |
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// set backoff (no time can pass in this state) |
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// probability depends on which transmission this is (cd1) |
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[] s1=2 & cd1=1 -> 1/2 : (s1'=3) & (bc1'=0) + 1/2 : (s1'=3) & (bc1'=1) ; |
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[] s1=2 & cd1=2 -> 1/4 : (s1'=3) & (bc1'=0) + 1/4 : (s1'=3) & (bc1'=1) + 1/4 : (s1'=3) & (bc1'=2) + 1/4 : (s1'=3) & (bc1'=3) ; |
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// wait until backoff counter reaches 0 then send again |
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[time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot) |
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[time] (s1=3) & (x1=slot) & (bc1>0) -> (x1'=1) & (bc1'=bc1-1); // let time pass (move slots) |
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[send1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=1) & (x1'=0); // finished backoff (bus appears free) |
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[busy1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // finished backoff (bus busy) |
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// once finished nothing matters |
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[time] (s1>=4) -> (x1'=0); |
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endmodule |
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//---------------------------------------------------------------------------------------------------------------------------- |
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// construct further stations through renaming |
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module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule |
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//---------------------------------------------------------------------------------------------------------------------------- |
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// reward structure for expected time |
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rewards "time" |
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[time] true : 1; |
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endrewards |
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//---------------------------------------------------------------------------------------------------------------------------- |
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// labels/formulae |
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label "all_delivered" = s1=4&s2=4; |
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label "one_delivered" = s1=4|s2=4; |
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label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2); |
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@ -0,0 +1,170 @@ |
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// firewire protocol with integer semantics |
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// dxp/gxn 14/06/01 |
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// CLOCKS |
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// x1 (x2) clock for node1 (node2) |
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// y1 and y2 (z1 and z2) clocks for wire12 (wire21) |
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mdp |
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// maximum and minimum delays |
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// fast |
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const int rc_fast_max = 85; |
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const int rc_fast_min = 76; |
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// slow |
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const int rc_slow_max = 167; |
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const int rc_slow_min = 159; |
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// delay caused by the wire length |
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const int delay = 3; |
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// probability of choosing fast |
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const double fast = 0.5; |
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const double slow=1-fast; |
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module wire12 |
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// local state |
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w12 : [0..9]; |
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// 0 - empty |
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// 1 - rec_req |
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// 2 - rec_req_ack |
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// 3 - rec_ack |
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// 4 - rec_ack_idle |
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// 5 - rec_idle |
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// 6 - rec_idle_req |
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// 7 - rec_ack_req |
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// 8 - rec_req_idle |
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// 9 - rec_idle_ack |
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// clock for wire12 |
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y1 : [0..delay+1]; |
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y2 : [0..delay+1]; |
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// empty |
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// do not need y1 and y2 to increase as always reset when this state is left |
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// similarly can reset y1 and y2 when we re-enter this state |
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[snd_req12] w12=0 -> (w12'=1) & (y1'=0) & (y2'=0); |
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[snd_ack12] w12=0 -> (w12'=3) & (y1'=0) & (y2'=0); |
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[snd_idle12] w12=0 -> (w12'=5) & (y1'=0) & (y2'=0); |
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[time] w12=0 -> (w12'=w12); |
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// rec_req |
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[snd_req12] w12=1 -> (w12'=1); |
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[rec_req12] w12=1 -> (w12'=0) & (y1'=0) & (y2'=0); |
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[snd_ack12] w12=1 -> (w12'=2) & (y2'=0); |
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[snd_idle12] w12=1 -> (w12'=8) & (y2'=0); |
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[time] w12=1 & y2<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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// rec_req_ack |
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[snd_ack12] w12=2 -> (w12'=2); |
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[rec_req12] w12=2 -> (w12'=3); |
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[time] w12=2 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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// rec_ack |
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[snd_ack12] w12=3 -> (w12'=3); |
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[rec_ack12] w12=3 -> (w12'=0) & (y1'=0) & (y2'=0); |
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[snd_idle12] w12=3 -> (w12'=4) & (y2'=0); |
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[snd_req12] w12=3 -> (w12'=7) & (y2'=0); |
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[time] w12=3 & y2<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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// rec_ack_idle |
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[snd_idle12] w12=4 -> (w12'=4); |
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[rec_ack12] w12=4 -> (w12'=5); |
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[time] w12=4 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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// rec_idle |
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[snd_idle12] w12=5 -> (w12'=5); |
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[rec_idle12] w12=5 -> (w12'=0) & (y1'=0) & (y2'=0); |
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[snd_req12] w12=5 -> (w12'=6) & (y2'=0); |
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[snd_ack12] w12=5 -> (w12'=9) & (y2'=0); |
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[time] w12=5 & y2<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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// rec_idle_req |
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[snd_req12] w12=6 -> (w12'=6); |
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[rec_idle12] w12=6 -> (w12'=1); |
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[time] w12=6 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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// rec_ack_req |
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[snd_req12] w12=7 -> (w12'=7); |
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[rec_ack12] w12=7 -> (w12'=1); |
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[time] w12=7 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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// rec_req_idle |
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[snd_idle12] w12=8 -> (w12'=8); |
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[rec_req12] w12=8 -> (w12'=5); |
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[time] w12=8 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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// rec_idle_ack |
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[snd_ack12] w12=9 -> (w12'=9); |
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[rec_idle12] w12=9 -> (w12'=3); |
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[time] w12=9 & y1<delay -> (y1'=min(y1+1,delay+1)) & (y2'=min(y2+1,delay+1)); |
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endmodule |
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module node1 |
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// clock for node1 |
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x1 : [0..168]; |
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// local state |
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s1 : [0..8]; |
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// 0 - root contention |
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// 1 - rec_idle |
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// 2 - rec_req_fast |
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// 3 - rec_req_slow |
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// 4 - rec_idle_fast |
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// 5 - rec_idle_slow |
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// 6 - snd_req |
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// 7- almost_root |
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// 8 - almost_child |
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// added resets to x1 when not considered again until after rest |
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// removed root and child (using almost root and almost child) |
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// root contention immediate state) |
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[snd_idle12] s1=0 -> fast : (s1'=2) & (x1'=0) + slow : (s1'=3) & (x1'=0); |
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[rec_idle21] s1=0 -> (s1'=1); |
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// rec_idle immediate state) |
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[snd_idle12] s1=1 -> fast : (s1'=4) & (x1'=0) + slow : (s1'=5) & (x1'=0); |
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[rec_req21] s1=1 -> (s1'=0); |
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// rec_req_fast |
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[rec_idle21] s1=2 -> (s1'=4); |
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[snd_ack12] s1=2 & x1>=rc_fast_min -> (s1'=7) & (x1'=0); |
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[time] s1=2 & x1<rc_fast_max -> (x1'=min(x1+1,168)); |
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// rec_req_slow |
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[rec_idle21] s1=3 -> (s1'=5); |
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[snd_ack12] s1=3 & x1>=rc_slow_min -> (s1'=7) & (x1'=0); |
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[time] s1=3 & x1<rc_slow_max -> (x1'=min(x1+1,168)); |
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// rec_idle_fast |
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[rec_req21] s1=4 -> (s1'=2); |
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[snd_req12] s1=4 & x1>=rc_fast_min -> (s1'=6) & (x1'=0); |
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[time] s1=4 & x1<rc_fast_max -> (x1'=min(x1+1,168)); |
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// rec_idle_slow |
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[rec_req21] s1=5 -> (s1'=3); |
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[snd_req12] s1=5 & x1>=rc_slow_min -> (s1'=6) & (x1'=0); |
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[time] s1=5 & x1<rc_slow_max -> (x1'=min(x1+1,168)); |
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// snd_req |
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// do not use x1 until reset (in state 0 or in state 1) so do not need to increase x1 |
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// also can set x1 to 0 upon entering this state |
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[rec_req21] s1=6 -> (s1'=0); |
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[rec_ack21] s1=6 -> (s1'=8); |
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[time] s1=6 -> (s1'=s1); |
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// almost root (immediate) |
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// loop in final states to remove deadlock |
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[] s1=7 & s2=8 -> (s1'=s1); |
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[] s1=8 & s2=7 -> (s1'=s1); |
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[time] s1=7 -> (s1'=s1); |
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[time] s1=8 -> (s1'=s1); |
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endmodule |
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|
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// construct remaining automata through renaming |
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module wire21=wire12[w12=w21, y1=z1, y2=z2, |
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snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21, |
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rec_req12=rec_req21, rec_idle12=rec_idle21, rec_ack12=rec_ack21] |
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endmodule |
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module node2=node1[s1=s2, s2=s1, x1=x2, |
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rec_req21=rec_req12, rec_idle21=rec_idle12, rec_ack21=rec_ack12, |
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snd_req12=snd_req21, snd_idle12=snd_idle21, snd_ack12=snd_ack21] |
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endmodule |
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// reward structures |
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// time |
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rewards "time" |
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[time] true : 1; |
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endrewards |
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// time nodes sending |
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rewards "time_sending" |
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[time] (w12>0 | w21>0) : 1; |
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endrewards |
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label "elected" = ((s1=8) & (s2=7)) | ((s1=7) & (s2=8)); |
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@ -0,0 +1,91 @@ |
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// asynchronous leader election |
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// 4 processes |
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// gxn/dxp 29/01/01 |
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mdp |
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const int N = 3; // number of processes |
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//---------------------------------------------------------------------------------------------------------------------------- |
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module process1 |
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// COUNTER |
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c1 : [0..3-1]; |
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// STATES |
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s1 : [0..4]; |
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// 0 make choice |
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// 1 have not received neighbours choice |
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// 2 active |
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// 3 inactive |
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// 4 leader |
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// PREFERENCE |
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p1 : [0..1]; |
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// VARIABLES FOR SENDING AND RECEIVING |
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receive1 : [0..2]; |
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// not received anything |
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// received choice |
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// received counter |
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sent1 : [0..2]; |
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// not send anything |
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// sent choice |
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// sent counter |
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|
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// pick value |
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[] (s1=0) -> 0.5 : (s1'=1) & (p1'=0) + 0.5 : (s1'=1) & (p1'=1); |
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|
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// send preference |
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[p12] (s1=1) & (sent1=0) -> (sent1'=1); |
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// receive preference |
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// stay active |
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[p31] (s1=1) & (receive1=0) & !( (p1=0) & (p3=1) ) -> (s1'=2) & (receive1'=1); |
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// become inactive |
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[p31] (s1=1) & (receive1=0) & (p1=0) & (p3=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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[c31] (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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[c31] (s1=2) & (receive1=1) & (sent1=2) & (c3=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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[c31] (s1=2) & (receive1=1) & (sent1=2) & (c3<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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[p31] (s1=3) & (receive1=0) -> (p1'=p3) & (receive1'=1); |
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// receive counter |
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[c31] (s1=3) & (receive1=1) & (c3<N-1) -> (c1'=c3+1) & (receive1'=2); |
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|
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// done |
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[done] (s1=4) -> (s1'=s1); |
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// add loop for processes who are inactive |
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[done] (s1=3) -> (s1'=s1); |
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|
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endmodule |
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|
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//---------------------------------------------------------------------------------------------------------------------------- |
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|
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// construct further stations through renaming |
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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 |
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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 |
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|
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//---------------------------------------------------------------------------------------------------------------------------- |
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|
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//---------------------------------------------------------------------------------------------------------------------------- |
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formula leaders = (s1=4?1:0)+(s2=4?1:0)+(s3=4?1:0); |
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label "elected" = s1=4|s2=4|s3=4; |
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|
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@ -0,0 +1,40 @@ |
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// sum of two dice as the asynchronous parallel composition of |
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// two copies of Knuth's model of a fair die using only fair coins |
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|
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mdp |
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|
|||
module die1 |
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|
|||
// local state |
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s1 : [0..7] init 0; |
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// value of the dice |
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d1 : [0..6] init 0; |
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|
|||
[] s1=0 -> 0.5 : (s1'=1) + 0.5 : (s1'=2); |
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[] s1=1 -> 0.5 : (s1'=3) + 0.5 : (s1'=4); |
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[] s1=2 -> 0.5 : (s1'=5) + 0.5 : (s1'=6); |
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[] s1=3 -> 0.5 : (s1'=1) + 0.5 : (s1'=7) & (d1'=1); |
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[] s1=4 -> 0.5 : (s1'=7) & (d1'=2) + 0.5 : (s1'=7) & (d1'=3); |
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[] s1=5 -> 0.5 : (s1'=7) & (d1'=4) + 0.5 : (s1'=7) & (d1'=5); |
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[] s1=6 -> 0.5 : (s1'=2) + 0.5 : (s1'=7) & (d1'=6); |
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[] s1=7 & s2=7 -> 1: (s1'=7); |
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endmodule |
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|
|||
module die2 = die1 [ s1=s2, s2=s1, d1=d2 ] endmodule |
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|
|||
rewards "coinflips" |
|||
[] s1<7 | s2<7 : 1; |
|||
endrewards |
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|
|||
label "done" = s1=7 & s2=7; |
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label "two" = s1=7 & s2=7 & d1+d2=2; |
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label "three" = s1=7 & s2=7 & d1+d2=3; |
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label "four" = s1=7 & s2=7 & d1+d2=4; |
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label "five" = s1=7 & s2=7 & d1+d2=5; |
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label "six" = s1=7 & s2=7 & d1+d2=6; |
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label "seven" = s1=7 & s2=7 & d1+d2=7; |
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label "eight" = s1=7 & s2=7 & d1+d2=8; |
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label "nine" = s1=7 & s2=7 & d1+d2=9; |
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label "ten" = s1=7 & s2=7 & d1+d2=10; |
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label "eleven" = s1=7 & s2=7 & d1+d2=11; |
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label "twelve" = s1=7 & s2=7 & d1+d2=12; |
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@ -0,0 +1,13 @@ |
|||
mdp |
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|
|||
module station1 |
|||
s1 : [0..12] init 0; |
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|
|||
// [] s1=0 -> (s1'=8) ; |
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|
|||
[] s1=1 -> (s1'=1); |
|||
[] s1=1 -> (s1'=1); |
|||
|
|||
//[] s1=8 -> (s1'=8); |
|||
|
|||
endmodule |
|||
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