Undecidable verification problems for programs with unreliable channels
Information and Computation
On Communicating Finite-State Machines
Journal of the ACM (JACM)
Probabilistic Lossy Channel Systems
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Verification of probabilistic systems with faulty communication
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Model checking lossy channels systems is probably decidable
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Mixing Lossy and Perfect Fifo Channels
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Verification of probabilistic systems with faulty communication
Information and Computation
Post embedding problem is not primitive recursive, with applications to channel systems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Lossy counter machines decidability cheat sheet
RP'10 Proceedings of the 4th international conference on Reachability problems
FORTE'06 Proceedings of the 26th IFIP WG 6.1 international conference on Formal Techniques for Networked and Distributed Systems
Computable fixpoints in well-structured symbolic model checking
Formal Methods in System Design
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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 communicate over unbounded lossy FIFO channels. Abdulla and Jonsson have shown that safety properties are decidable while progress properties are undecidable 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 consider a model of probabilistic lossy channel systems, where messages can be lost only during send transitions. In contrast to the model of Baier and Engelen, once a message is successfully sent to channel, it can only be removed through a transition which receives the message. We show that checking whether safety properties hold with probability 1 is undecidable for this model. Our proof depends upon simulating a perfect channel, with a high degree of confidence, using lossy channels.