// asynchronous leader election // 4 processes // gxn/dxp 29/01/01 mdp const N=4; // number of processes module process1 // COUNTER c1 : [0..N-1]; // STATES s1 : [0..4]; // 0 make choice // 1 have not received neighbours choice // 2 active // 3 inactive // 4 leader // PREFERENCE p1 : [0..1]; // VARIABLES FOR SENDING AND RECEIVING receive1 : [0..2]; // not received anything // received choice // received counter sent1 : [0..2]; // not send anything // sent choice // sent counter // pick value [] (s1=0) -> 0.5 : (s1'=1) & (p1'=0) + 0.5 : (s1'=1) & (p1'=1); // send preference [p12] (s1=1) & (sent1=0) -> (sent1'=1); // receive preference // stay active [p41] (s1=1) & (receive1=0) & !( (p1=0) & (p4=1) ) -> (s1'=2) & (receive1'=1); // become inactive [p41] (s1=1) & (receive1=0) & (p1=0) & (p4=1) -> (s1'=3) & (receive1'=1); // send preference (can now reset preference) [p12] (s1=2) & (sent1=0) -> (sent1'=1) & (p1'=0); // send counter (already sent preference) // not received counter yet [c12] (s1=2) & (sent1=1) & (receive1=1) -> (sent1'=2); // received counter (pick again) [c12] (s1=2) & (sent1=1) & (receive1=2) -> (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); // receive counter and not sent yet (note in this case do not pass it on as will send own counter) [c41] (s1=2) & (receive1=1) & (sent1<2) -> (receive1'=2); // receive counter and sent counter // only active process (decide) [c41] (s1=2) & (receive1=1) & (sent1=2) & (c4=N-1) -> (s1'=4) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); // other active process (pick again) [c41] (s1=2) & (receive1=1) & (sent1=2) & (c4 (s1'=0) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); // send preference (must have received preference) and can now reset [p12] (s1=3) & (receive1>0) & (sent1=0) -> (sent1'=1) & (p1'=0); // send counter (must have received counter first) and can now reset [c12] (s1=3) & (receive1=2) & (sent1=1) -> (s1'=3) & (p1'=0) & (c1'=0) & (sent1'=0) & (receive1'=0); // receive preference [p41] (s1=3) & (receive1=0) -> (p1'=p4) & (receive1'=1); // receive counter [c41] (s1=3) & (receive1=1) & (c4 (c1'=c4+1) & (receive1'=2); // done [done] (s1=4) -> (s1'=s1); // add loop for processes who are inactive [done] (s1=3) -> (s1'=s1); endmodule module process2=process1[s1=s2,p1=p2,c1=c2,sent1=sent2,receive1=receive2,p12=p23,p41=p12,c12=c23,c41=c12,p4=p1,c4=c1] endmodule module process3=process1[s1=s3,p1=p3,c1=c3,sent1=sent3,receive1=receive3,p12=p34,p41=p23,c12=c34,c41=c23,p4=p2,c4=c2] endmodule module process4=process1[s1=s4,p1=p4,c1=c4,sent1=sent4,receive1=receive4,p12=p41,p41=p34,c12=c41,c41=c34,p4=p3,c4=c3] endmodule // reward - expected number of rounds (equals the number of times a process receives a counter) rewards "rounds" [c12] true : 1; endrewards