dehnert
12 years ago
3 changed files with 186 additions and 0 deletions
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60examples/mdp/consensus/coin2.nm
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62examples/mdp/consensus/coin4.nm
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64examples/mdp/consensus/coin6.nm
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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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// constants |
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const int N=2; |
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const int K; |
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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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// 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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// local coin |
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coin1 : [0..1]; |
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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) -> (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) -> (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) -> (pc1'=3) & (coin1'=0); |
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// decide heads |
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[] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); |
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// flip again |
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[] (pc1=2) & (counter>left) & (counter<right) -> (pc1'=0); |
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// loop (all loop together when done) |
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[done] (pc1=3) -> (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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// 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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// constants |
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const int N=4; |
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const int K; |
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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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// 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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// 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) -> (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) -> (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) -> (pc1'=3) & (coin1'=0); |
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// decide heads |
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[] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); |
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// flip again |
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[] (pc1=2) & (counter>left) & (counter<right) -> (pc1'=0); |
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// loop (all loop together when done) |
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[done] (pc1=3) -> (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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module process3 = process1[pc1=pc3,coin1=coin3] endmodule |
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module process4 = process1[pc1=pc4,coin1=coin4] endmodule |
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// labels |
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label "finished" = pc1=3 & pc2=3 & pc3=3 & pc4=3 ; |
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label "all_coins_equal_0" = coin1=0 & coin2=0 & coin3=0 & coin4=0 ; |
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label "all_coins_equal_1" = coin1=1 & coin2=1 & coin3=1 & coin4=1 ; |
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label "agree" = coin1=coin2 & coin2=coin3 & coin3=coin4 ; |
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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 +1,64 @@ |
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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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// constants |
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const int N=6; |
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const int K; |
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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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// 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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// local coin |
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coin1 : [0..1]; |
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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) -> (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) -> (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) -> (pc1'=3) & (coin1'=0); |
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// decide heads |
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[] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); |
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// flip again |
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[] (pc1=2) & (counter>left) & (counter<right) -> (pc1'=0); |
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// loop (all loop together when done) |
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[done] (pc1=3) -> (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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module process3 = process1[pc1=pc3,coin1=coin3] endmodule |
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module process4 = process1[pc1=pc4,coin1=coin4] endmodule |
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module process5 = process1[pc1=pc5,coin1=coin5] endmodule |
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module process6 = process1[pc1=pc6,coin1=coin6] endmodule |
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// labels |
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label "finished" = pc1=3 & pc2=3 & pc3=3 & pc4=3 & pc5=3 & pc6=3 ; |
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label "all_coins_equal_0" = coin1=0 & coin2=0 & coin3=0 & coin4=0 & coin5=0 & coin6=0 ; |
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label "all_coins_equal_1" = coin1=1 & coin2=1 & coin3=1 & coin4=1 & coin5=1 & coin6=1 ; |
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label "agree" = coin1=coin2 & coin2=coin3 & coin3=coin4 & coin4=coin5 & coin5=coin6 ; |
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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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