```// Lehmann-Rabin algorithm [LR82] (dining philosophers)
// we suppose an action takes 1 time unit
// an a process can wait at most K time units before making a transition
// gxn/dxp 01/02/00

mdp

// CONSTANTS
const K;

// COUNTER FORMULAE
// ci number of steps since process last moved
// removing trying and remainder states since
// these are controlled by the process not the adversary

// process can go if it does not stop one of the other processes round counter reaching K+1
// added complication if two processes counter equals K-1, then if neither makes a transition
// both reach K, and hence one must reach K+1 which we must disallow
formula can1 = !((c2=K) | (c3=K) | ((c2=K-1) & (c3=K-1)));
formula can2 = !((c1=K) | (c3=K) | ((c1=K-1) & (c3=K-1)));
formula can3 = !((c1=K) | (c2=K) | ((c1=K-1) & (c2=K-1)));

// when a process moves the counters of the other processes increase
// but only when they are not in trying or remainder
formula count1  = (p1!=13) & (p1!=0);
formula count2  = (p2!=13) & (p2!=0);
formula count3  = (p3!=13) & (p3!=0);
formula ncount1 = (p1=13) | (p1=0);
formula ncount2 = (p2=13) | (p2=0);
formula ncount3 = (p3=13) | (p3=0);

module counter

c1 : [0..K];
c2 : [0..K];
c3 : [0..K];

// process 1 moves
[s1] count2  & count3  & can1 -> (c1'=0) & (c2'=c2+1) & (c3'=c3+1);
[s1] ncount2 & count3  & can1 -> (c1'=0) & (c3'=c3+1);
[s1] count2  & ncount3 & can1 -> (c1'=0) & (c2'=c2+1);
[s1] ncount2 & ncount3 & can1 -> (c1'=0);
// process 2 moves
[s2] count1  & count3  & can2 -> (c2'=0) & (c1'=c1+1) & (c3'=c3+1);
[s2] ncount1 & count3  & can2 -> (c2'=0) & (c3'=c3+1);
[s2] count1  & ncount3 & can2 -> (c2'=0) & (c1'=c1+1);
[s2] ncount1 & ncount3 & can2 -> (c2'=0);
// process 3 moves
[s3] count1  & count2  & can3 -> (c3'=0) & (c1'=c1+1) & (c2'=c2+1);
[s3] ncount1 & count2  & can3 -> (c3'=0) & (c2'=c2+1);
[s3] count1  & ncount2 & can3 -> (c3'=0) & (c1'=c1+1);
[s3] ncount1 & ncount2 & can3 -> (c3'=0);

endmodule

// PHILOSOPHER 1
// atomic formule
// left fork and right fork free resp.
formula lfree = p2>=0&p2<=4|p2=6|p2=11|p2=13;
formula rfree = p3>=0&p3<=3|p3=5|p3=7|p3=12|p3=13;

module phil1

p1 : [0..13];

[s1] (p1=0) -> (p1'=0); // try
[s1] (p1=0) -> (p1'=1);
[s1] (p1=1) -> 0.5 : (p1'=2) + 0.5 : (p1'=3); // flip
[s1] (p1=2) &  lfree -> (p1'=4); // wl and l free
[s1] (p1=2) & !lfree -> (p1'=2); // wl and l taken
[s1] (p1=3) &  rfree -> (p1'=5); // wr and r free
[s1] (p1=3) & !rfree -> (p1'=3); // wr and r taken
[s1] (p1=4) &  rfree -> (p1'=8); // l and r free
[s1] (p1=4) & !rfree -> (p1'=6); // l and r taken
[s1] (p1=5) &  lfree -> (p1'=8); // r and l free
[s1] (p1=5) & !lfree -> (p1'=7); // r and l taken
[s1] (p1=6)  -> (p1'=1); // nr
[s1] (p1=7)  -> (p1'=1); // nl
[s1] (p1=8)  -> (p1'=9); // pre_crit
[s1] (p1=9)  -> (p1'=10); // crit
[s1] (p1=10) -> (p1'=11); // exit
[s1] (p1=10) -> (p1'=12);
[s1] (p1=11) -> (p1'=13); // put down left first
[s1] (p1=12) -> (p1'=13); // put down right first
[s1] (p1=13) -> (p1'=0); // remainder
[s1] (p1=13) -> (p1'=13);

endmodule

// construct further processes through renaming
module phil2=phil1 [p1=p2, p2=p3, p3=p1, s1=s2] endmodule
module phil3=phil1 [p1=p3, p2=p1, p3=p2, s1=s3] endmodule

// reward structure - number of steps
rewards "steps"
[s1] true : 1;
[s2] true : 1;
[s3] true : 1;
endrewards
```