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A Proof System for Compositional Verification of Probabilistic Concurrent Processes

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.
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https://hal.inria.fr/hal-00766384
Contributor : Matteo Mio <>
Submitted on : Tuesday, December 18, 2012 - 11:37:22 AM
Last modification on : Saturday, September 11, 2021 - 3:18:59 AM

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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. Foundations of Software Science and Computation Structures - 16th International Conference (FOSSACS 2013), Mar 2013, Rome, Italy. pp.161-176. ⟨hal-00766384⟩

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