LIPIcs.FSTTCS.2009.2323.pdf
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Verification and Refutation of Probabilistic Specifications via Games
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IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2009-12-14
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Mark Kattenbelt and Michael Huth. Verification and Refutation of Probabilistic Specifications via Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 251-262, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.FSTTCS.2009.2323
Abstract
We develop an abstraction-based framework to check probabilistic specifications of Markov Decision Processes (MDPs) using the stochastic two-player game abstractions (\ie ``games'') developed by Kwiatkowska et al.\ as a foundation. We define an abstraction preorder for these game abstractions which enables us to identify many new game abstractions for each MDP --- ranging from compact and imprecise to complex and precise. This added ability to trade precision for efficiency is crucial for scalable software model checking, as precise abstractions are expensive to construct in practice. Furthermore, we develop a four-valued probabilistic computation tree logic (PCTL) semantics for game abstractions. Together, the preorder and PCTL semantics comprise a powerful verification and refutation framework for arbitrary PCTL properties of MDPs.
Subject Classification
Keywords
- Probabilistic model checking
- Markov decision processes
- Abstraction preorder
- Stochastic two-player games
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