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Reasoning about probabilistic lossy channel Parosh Abdulla 1 , Christel Baier 2 , Purushothaman Iyer 3? , and Bengt Jonsson 1

Summary: Reasoning about probabilistic lossy channel
Parosh Abdulla 1 , Christel Baier 2 , Purushothaman Iyer 3? , and Bengt Jonsson 1
1 Dept of Computer Systems, Uppsala University, Uppsala, Sweden
2 Dept of Computer Science, University of Bonn, Bonn, Germany
3 Dept of Computer Science, North Carolina State University, Raleigh, NC 27695,
Abstract. We consider the problem of deciding whether an infinite­
state system (expressed as a Markov chain) satisfies a correctness prop­
erty with probability 1. This problem is, of course, undecidable for gen­
eral infinite­state systems. We focus our attention on the model of proba­
bilistic lossy channel systems consisting of finite­state processes that com­
municating over unbounded lossy FIFO channels. Abdulla and Jonsson
have shown that safety properties are decidable while progress properties
are not for non­probabilistic 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


Source: Abdulla, Parosh Aziz - Department of Information Technology, Uppsala Universitet


Collections: Computer Technologies and Information Sciences