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// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90]
// gxn/dxp 20/11/00
mdp
// constants
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) -> 0.5 : (coin1'=0) & (pc1'=1) + 0.5 : (coin1'=1) & (pc1'=1);
// write tails -1 (reset coin to add regularity)
[] (pc1=1) & (coin1=0) & (counter>0) -> 1 : (counter'=counter-1) & (pc1'=2) & (coin1'=0);
// write heads +1 (reset coin to add regularity)
[] (pc1=1) & (coin1=1) & (counter<range) -> 1 : (counter'=counter+1) & (pc1'=2) & (coin1'=0);
// check
// decide tails
[] (pc1=2) & (counter<=left) -> 1 : (pc1'=3) & (coin1'=0);
// decide heads
[] (pc1=2) & (counter>=right) -> 1 : (pc1'=3) & (coin1'=1);
// flip again
[] (pc1=2) & (counter>left) & (counter<right) -> 1 : (pc1'=0);
// loop (all loop together when done)
[done] (pc1=3) -> 1 : (pc1'=3);
endmodule
// construct remaining processes through renaming
module process2 = process1[pc1=pc2,coin1=coin2] endmodule
// labels
label "finished" = pc1=3 & pc2=3 ;
label "all_coins_equal_0" = coin1=0 & coin2=0 ;
label "all_coins_equal_1" = coin1=1 & coin2=1 ;
label "agree" = coin1=coin2 ;
// rewards
rewards "steps"
true : 1;
endrewards