Simulating perfect channels with probabilistic lossy channels

Authors:
Parosh Abdulla;Christel Baier;S. Purushothaman Iyer;Bengt Jonsson
Affiliations:
Department of Computer Systems, Uppsala University, SE-751 05 Uppsala, Sweden;Department of Computer Science, University of Bonn, 53117 Bonn, Germany;Department of Computer Science, North Carolina State University, Raleigh, NC;Department of Computer Systems, Uppsala University, SE-751 05 Uppsala, Sweden
Venue:
Information and Computation
Year:
2005

Citing 5
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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 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.