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Conference Papers Year : 2017

Reachability in Parametric Interval Markov Chains Using Constraints

Abstract

Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs – consistency, qualitative reachability and quantitative reachability – that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results.
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Dates and versions

hal-01591036 , version 1 (20-09-2017)

Identifiers

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Anicet Bart, Benoit Delahaye, Didier Lime, Eric Monfroy, Charlotte Truchet. Reachability in Parametric Interval Markov Chains Using Constraints. 14th International Conference on Quantitative Evaluation of SysTems, Sep 2017, Berlin, Germany. pp.527 - 189, ⟨10.1007/978-3-319-66335-7_11⟩. ⟨hal-01591036⟩
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