A Proof System for Compositional Verification of Probabilistic Concurrent Processes

Matteo Mio, Alex Simpson

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We present a formal proof system for compositional verification 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 quantitative interpretation. A key feature is that the probabilistic scenario is handled by introducing the notion of Markov proof, according to which proof trees contain probabilistic branches and are required to satisfy a condition formulated by interpreting them as Markov Decision Processes. 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.
Original languageEnglish
Title of host publicationFoundations of Software Science and Computation Structures
Subtitle of host publication16th International Conference, FOSSACS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings
EditorsFrank Pfenning
PublisherSpringer-Verlag GmbH
Number of pages16
ISBN (Electronic)978-3-642-37075-5
ISBN (Print)978-3-642-37074-8
Publication statusPublished - 2013

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin / Heidelberg
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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