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Fair termination for parameterized probabilistic concurrent systems. (English) Zbl 1452.68127
Legay, Axel (ed.) et al., Tools and algorithms for the construction and analysis of systems. 23rd international conference, TACAS 2017, held as part of the European joint conferences on theory and practice of software, ETAPS 2017, Uppsala, Sweden, April 22–29, 2017. Proceedings. Part I. Berlin: Springer. Lect. Notes Comput. Sci. 10205, 499-517 (2017).
Summary: We consider the problem of automatically verifying that a parameterized family of probabilistic concurrent systems terminates with probability one for all instances against adversarial schedulers. A parameterized family defines an infinite-state system: for each number n, the family consists of an instance with \(n\) finite-state processes. In contrast to safety, the parameterized verification of liveness is currently still considered extremely challenging especially in the presence of probabilities in the model. One major challenge is to provide a sufficiently powerful symbolic framework. One well-known symbolic framework for the parameterized verification of non-probabilistic concurrent systems is regular model checking. Although the framework was recently extended to probabilistic systems, incorporating fairness in the framework – often crucial for verifying termination – has been especially difficult due to the presence of an infinite number of fairness constraints (one for each process). Our main contribution is a systematic, regularity-preserving, encoding of finitary fairness (a realistic notion of fairness proposed by Alur and Henzinger) in the framework of regular model checking for probabilistic parameterized systems. Our encoding reduces termination with finitary fairness to verifying parameterized termination without fairness over probabilistic systems in regular model checking (for which a verification framework already exists). We show that our algorithm could verify termination for many interesting examples from distributed algorithms (Herman’s protocol) and evolutionary biology (Moran process, cell cycle switch), which do not hold under the standard notion of fairness. To the best of our knowledge, our algorithm is the first fully-automatic method that can prove termination for these examples.
For the entire collection see [Zbl 1360.68015].
MSC:
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
68Q60 Specification and verification (program logics, model checking, etc.)
68Q87 Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)
Software:
FAST; PRISM
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