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//Randomised Consensus Protocol
mdp const double p1; // in [0.2 , 0.8] const double p2; // in [0.2 , 0.8]
const int N=2; const int K=2; const int range = 2*(K+1)*N; const int counter_init = (K+1)*N; const int left = N; const int right = 2*(K+1)*N - N;
// shared coin global counter : [0..range] init counter_init;
module process1 // program counter pc1 : [0..3]; // 0 - flip // 1 - write // 2 - check // 3 - finished // local coin coin1 : [0..1];
// flip coin [] (pc1=0) -> p1 : (coin1'=0) & (pc1'=1) + 1 - p1 : (coin1'=1) & (pc1'=1); // write tails -1 (reset coin to add regularity) [] (pc1=1) & (coin1=0) & (counter>0) -> (counter'=counter-1) & (pc1'=2) & (coin1'=0); // write heads +1 (reset coin to add regularity) [] (pc1=1) & (coin1=1) & (counter<range) -> (counter'=counter+1) & (pc1'=2) & (coin1'=0); // check // decide tails [] (pc1=2) & (counter<=left) -> (pc1'=3) & (coin1'=0); // decide heads [] (pc1=2) & (counter>=right) -> (pc1'=3) & (coin1'=1); // flip again [] (pc1=2) & (counter>left) & (counter<right) -> (pc1'=0); // loop (all loop together when done) [done] (pc1=3) -> (pc1'=3);
endmodule
module process2 = process1[pc1=pc2,coin1=coin2,p1=p2] endmodule label "finished" = pc1=3 &pc2=3 ; label "all_coins_equal_1" = coin1=1 &coin2=1 ; rewards "steps" true : 1; endrewards
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