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27 lines
1.6 KiB
27 lines
1.6 KiB
// Mutual exclusion: at any time t there is at most one process in its critical section phase
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num_procs_in_crit <= 1
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// Liveness: if a process is trying, then eventually a process enters the critical section
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"one_trying" => P>=1 [ F "one_critical" ]
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// weaker version of k-bounded waiting: minimum probability process enters the criticial section given it draws
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Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical"}{min} ]
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// filter expresses the fact that we are only interested in the probability for states in which
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// - process is going to make a draw (draw1=1)
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// - no process is in the critical section (otherwise probability is clearly 0)
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// and we take the minimum value over this set of states
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// probability above is zero which is due to the fact that in certain states the adversary can
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// use the values of the draw variables of other processes to prevent the process from entering
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// the criticial section
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// this does not quite disprove Rabin's bounded waiting property as one is starting
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// from the state the process decides to enter the round and one does not take into account
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// the probability of reaching this state (this does have an influence as the results
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// for the properties below show that to get the probability 0 one of the other processes
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//must have already randomly picked a high value for its bi)
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// to demonstrate this fact we restrict attention to states where these values
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// are restricted,i.e. where the values of the bi variables are bounded
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const int k;
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Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical" & maxb<=k}{min} ]
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