On randomization in sequential and distributed algorithms
ACM Computing Surveys (CSUR)
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
Bisimulation and Other Undecidable Equivalences for Lossy Channel Systems
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Verifying Randomized Byzantine Agreement
FORTE '02 Proceedings of the 22nd IFIP WG 6.1 International Conference Houston on Formal Techniques for Networked and Distributed Systems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Termination Problems in Chemical Kinetics
CONCUR '08 Proceedings of the 19th international conference on Concurrency Theory
Sliding Window Abstraction for Infinite Markov Chains
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Logical implementation of uncertain agents
EPIA'05 Proceedings of the 12th Portuguese conference on Progress in Artificial Intelligence
On the decidability of temporal properties of probabilistic pushdown automata
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
A Basic Logic for Reasoning about Connector Reconfiguration
Fundamenta Informaticae - Behavior of Composed Concurrent Systems: Logic and Reasoning
Branching-time model-checking of probabilistic pushdown automata
Journal of Computer and System Sciences
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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 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.