dtmc // probability of forwarding const double PF = 0.8; const double notPF = .2; // must be 1-PF // probability that a crowd member is bad const double badC = .167; // probability that a crowd member is good const double goodC = 0.833; // Total number of protocol runs to analyze const int TotalRuns = 5; // size of the crowd const int CrowdSize = 5; module crowds // protocol phase phase: [0..4] init 0; // crowd member good (or bad) good: bool init false; // number of protocol runs runCount: [0..TotalRuns] init 0; // observe_i is the number of times the attacker observed crowd member i observe0: [0..TotalRuns] init 0; observe1: [0..TotalRuns] init 0; observe2: [0..TotalRuns] init 0; observe3: [0..TotalRuns] init 0; observe4: [0..TotalRuns] init 0; // the last seen crowd member lastSeen: [0..CrowdSize - 1] init 0; // get the protocol started [] phase=0 & runCount 1: (phase'=1) & (runCount'=runCount+1) & (lastSeen'=0); // decide whether crowd member is good or bad according to given probabilities [] phase=1 -> goodC : (phase'=2) & (good'=true) + badC : (phase'=2) & (good'=false); // if the current member is a good member, update the last seen index (chosen uniformly) [] phase=2 & good -> 1/5 : (lastSeen'=0) & (phase'=3) + 1/5 : (lastSeen'=1) & (phase'=3) + 1/5 : (lastSeen'=2) & (phase'=3) + 1/5 : (lastSeen'=3) & (phase'=3) + 1/5 : (lastSeen'=4) & (phase'=3); // if the current member is a bad member, record the most recently seen index [] phase=2 & !good & lastSeen=0 & observe0 < TotalRuns -> 1: (observe0'=observe0+1) & (phase'=4); [] phase=2 & !good & lastSeen=1 & observe1 < TotalRuns -> 1: (observe1'=observe1+1) & (phase'=4); [] phase=2 & !good & lastSeen=2 & observe2 < TotalRuns -> 1: (observe2'=observe2+1) & (phase'=4); [] phase=2 & !good & lastSeen=3 & observe3 < TotalRuns -> 1: (observe3'=observe3+1) & (phase'=4); [] phase=2 & !good & lastSeen=4 & observe4 < TotalRuns -> 1: (observe4'=observe4+1) & (phase'=4); // good crowd members forward with probability PF and deliver otherwise [] phase=3 -> PF : (phase'=1) + notPF : (phase'=4); // deliver the message and start over [] phase=4 -> 1: (phase'=0); endmodule label "observe0Greater1" = observe0>1; label "observe1Greater1" = observe1>1; label "observe2Greater1" = observe2>1; label "observe3Greater1" = observe3>1; label "observe4Greater1" = observe4>1; label "observeIGreater1" = observe1>1|observe2>1|observe3>1|observe4>1; label "observeOnlyTrueSender" = observe0>1&observe1<=1 & observe2<=1 & observe3<=1 & observe4<=1;