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23 lines
1.7 KiB
23 lines
1.7 KiB
// mention that Rabin property is not well defined (see Saias thesis)
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// minimum probability process enters the criticial section
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// only interested in the probability in states for 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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Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical"}{min} ]
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// probability above is zero which is due to the fact that the adversary can use the values
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// of the state variables of the other processes
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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 doesnot 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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Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical" & maxb<6}{min} ]
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Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical" & maxb<5}{min} ]
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Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical" & maxb<4}{min} ]
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Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical" & maxb<3}{min} ]
Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical" & maxb<2}{min} ]
Pmin=?[ !"one_critical" U (p1=2) {draw1=1 & !"one_critical" & maxb<1}{min} ]
// liveness (eventially a process enters its critical section
// since we have removed the loops this holds with probability 1 even without fairness
Pmin=?[F p1=2 | p2=2 | p3=2 ]
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