Reasoning about Probabilistic Lossy Channel Systems

Abstract

We consider the problem of deciding whether an infinite-state system (expressed as a Markov chain) satisfies a correctness property with probability 1. This problem is, of course, undecidable for general infinite-state systems. We focus our attention on the model of probabilistic lossy channel systems consisting of finite-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 “sufficiently 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 “sufficiently 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 confidence, using lossy channels.KeywordsModel CheckGlobal StateSafety PropertyReachability ProblemMessage LossThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.