// COIN FLIPPING PROTOCOL FOR POLYNOMIAL RANDOMIZED CONSENSUS [AH90]
// gxn/dxp 20/11/00

mdp

// constants
const int N=8;
const int K;
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) -> (counter'=counter-1) & (pc1'=2) & (coin1'=0);
[] (pc1=1) & (coin1=1) & (counter<range) -> (counter'=counter+1) & (pc1'=2) & (coin1'=0);
// check
// decide tails
[] (pc1=2) & (counter<=left) -> (pc1'=3) & (coin1'=0);
[] (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

// construct remaining processes through renaming
module process2 = process1[pc1=pc2,coin1=coin2] endmodule
module process3 = process1[pc1=pc3,coin1=coin3] endmodule
module process4 = process1[pc1=pc4,coin1=coin4] endmodule
module process5 = process1[pc1=pc5,coin1=coin5] endmodule
module process6 = process1[pc1=pc6,coin1=coin6] endmodule
module process7 = process1[pc1=pc7,coin1=coin7] endmodule
module process8 = process1[pc1=pc8,coin1=coin8] endmodule

// labels
label "finished" = pc1=3 & pc2=3 & pc3=3 & pc4=3 & pc5=3 & pc6=3 & pc7=3 & pc8=3 ;
label "all_coins_equal_0" = coin1=0 & coin2=0 & coin3=0 & coin4=0 & coin5=0 & coin6=0 & coin7=0 & coin8=0 ;
label "all_coins_equal_1" = coin1=1 & coin2=1 & coin3=1 & coin4=1 & coin5=1 & coin6=1 & coin7=1 & coin8=1 ;
label "agree" = coin1=coin2 & coin2=coin3 & coin3=coin4 & coin4=coin5 & coin5=coin6 & coin6=coin7 & coin7=coin8 ;

// rewards
rewards "steps"
true : 1;
endrewards