A Proof System for Compositional Verification of Probabilistic Concurrent Processes

Matteo Mio 1, 2 Alex Simpson 3
1 COMETE - Concurrency, Mobility and Transactions
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR7161
Abstract : We present a formal proof system for compositional verifica- tion of probabilistic concurrent processes. Processes are specified using an SOS-style process algebra with probabilistic operators. Properties are expressed using a probabilistic modal μ-calculus. And the proof system is formulated as a sequent calculus in which sequents are given a quan- titative interpretation. A key feature is that the probabilistic scenario is handled by introducing the notion of Markov proof, by which each proof in the system is interpreted as a Markov Decision Process, with the proof only considered valid in the case that the value of the MDP is zero. We present simple but illustrative examples demonstrating the applicability of the approach to the compositional verification of infinite state processes. Our main result is the soundness of the proof system, which is proved by applying the coupling method from probability theory to the game semantics of the probabilistic modal μ-calculus.
Type de document :
Communication dans un congrès
Frank Pfenning. Foundations of Software Science and Computation Structures - 16th International Conference (FOSSACS 2013), Mar 2013, Rome, Italy. Springer, 7794, pp.161-176, 2013, Lecture Notes in Computer Science
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Contributeur : Matteo Mio <>
Soumis le : mardi 18 décembre 2012 - 11:37:22
Dernière modification le : jeudi 11 janvier 2018 - 06:22:14

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  • HAL Id : hal-00766384, version 1

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Matteo Mio, Alex Simpson. A Proof System for Compositional Verification of Probabilistic Concurrent Processes. Frank Pfenning. Foundations of Software Science and Computation Structures - 16th International Conference (FOSSACS 2013), Mar 2013, Rome, Italy. Springer, 7794, pp.161-176, 2013, Lecture Notes in Computer Science. 〈hal-00766384〉

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