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Undecidable Verification Problems for Programs with Unreliable Channels

Summary: Undecidable Verification Problems for Programs
with Unreliable Channels
Parosh Aziz Abdulla and Bengt Jonsson
Uppsala University, Dept. of Computer Systems
P.O. Box 325, 751 05 Uppsala, Sweden
E--mail:fparosh,bengtg@docs.uu.se \Lambda
We consider the verification of a particular class of infinite­state systems, namely
systems consisting of finite­state processes that communicate via unbounded lossy FIFO
channels. This class is able to model e.g. link protocols such as the Alternating Bit
Protocol and HDLC. In an earlier paper, we showed that several interesting verification
problems are decidable for this class of systems, namely (1) the reachability problem: is
a set of states reachable from some other state of the system, (2) safety property over
traces formulated as regular sets of allowed finite traces, and (3) eventuality properties:
do all computations of a system eventually reach a given set of states. In this paper, we
show that the following problems are undecidable, namely
ffl The model checking problem in propositional temporal logics such as Propositional
Linear Time Logic (PTL) and Computation Tree Logic (CTL).
ffl The problem of deciding eventuality properties with fair channels: do all compu­
tations eventually reach a given set of states if the unreliable channels are fair in


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


Collections: Computer Technologies and Information Sciences