We consider the problem of verifying correctness of finite state machines that communicate with each other over unbounded FIFO channels that are unreliable. Various problems of interest in verification of FIFO channels that can lose messages have been considered by Finkel and by Abdulla and Jonsson. We consider, in this paper, other possible unreliable behaviors of communication channels, viz., (a) duplication and (b) insertion errors. Furthermore, we also consider various combinations of duplication, insertion, and lossiness errors. Finite state machines that communicate over unbounded FIFO buffers are a model of computation that forms the backbone of the ISO standard protocol specification languages Estelle and SDL. While the assumption of a perfect communication medium is reasonable at the higher levels of the OSI protocol stack, the lower levels have to deal with an unreliable communication medium; hence our motivation for the present work. The verification problems that are of interest are reachability, unboundedness, deadlock, and model-checking against CTL*. All of these problems are undecidable for machines communicating over reliable unbounded FIFO channels. So it is perhaps surprising that some of these problems become decidable when unreliable channels are modeled. The contributions of this paper are (a) an investigation of solutions to these problems for machines with insertion errors, duplication errors, or a combination of duplication, insertion, and lossiness errors, and (b) a comparison of the relative expressive power of the various errors.

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This paper presents a mu-calculus-based modal logic for describing properties of reactive probabilistic labeled transition systems (RPLTSs) and develops a model-checking algorithm for determining whether or not states in finite-state RPLTSs satisfy formulas in the logic. The logic is based on the distinction between (probabilistic) "systems" and (nonprobabilistic) "observations": using the modal mu-calculus, one may specify sets of observations, and the semantics of our logic then enable statements to be made about the measures of such sets at various system states. The logic may be used to encode a variety of probabilistic modal and temporal logics; in addition, the model-checking problem for it may be reduced to the calculation of solutions to systems of non-linear equations. Finally, the logic induces an equivalence on RPLTSs that coincides with accepted notions of probabilistic bisimulation in the literature.

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