Reasoning about Probabilistic Lossy Channel Systems
نویسندگان
چکیده
We consider the problem of deciding whether an innnite-state system (expressed as a Markov chain) satisses a correctness property with probability 1. This problem is, of course, undecidable for general innnite-state systems. We focus our attention on the model of proba-bilistic lossy channel systems consisting of nite-state processes that communicating over unbounded lossy FIFO channels. Abdulla and Jonsson have shown that safety properties are decidable while progress properties are not for non-probabilistic lossy channel systems. Under assumptions of \suuciently high" probability of loss, Baier and Engelen have shown how to check whether a property holds of probabilistic lossy channel system with probability 1. In this paper we show that the problem of checking whether a progress property holds with probability 1 is undecidable, if the assumption about \suuciently high" probability of loss is omitted. More surprisingly, we show that checking whether safety properties hold with probability 1 is undecidable too. Our proof depends upon simulating a perfect channel, with a high degree of conndence, using lossy channels.
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