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International Symposium on Leveraging Applications of Formal Methods

ISoLA 2016: Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques pp 27–45Cite as

Survey of Statistical Verification of Linear Unbounded Properties: Model Checking and Distances

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9952))

Abstract

We survey statistical verification techniques aiming at linear properties with unbounded or infinite horizon, as opposed to properties of runs of fixed length. We discuss statistical model checking of Markov chains and Markov decision processes against reachability, unbounded-until, LTL and mean-payoff properties. Moreover, the respective strategies can be represented efficiently using statistical techniques. Further, we also discuss when it is possible to statistically estimate linear distances between Markov chains.

This research was partially supported by the Czech Science Foundation under grant agreement P202/12/G061.

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Notes

  1. 1.

    Formally, the measurable space of \(\omega \)-languages is given by the set \(\varSigma ^\omega \) equipped with a \(\sigma \)-algebra \(\mathcal F(\varSigma )\) generated by the set of cones \(\{w\varSigma ^\omega \mid w\in \varSigma ^*\}\). This ensures, for every measurable \(\omega \)-language X, that \(L^{-1}(X)\) is measurable in every MC.

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  1. Technische Universität München, Munich, Germany

    Jan Křetínský

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    Tiziana Margaria

  2. TU Dortmund, Dortmund, Germany

    Bernhard Steffen

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Křetínský, J. (2016). Survey of Statistical Verification of Linear Unbounded Properties: Model Checking and Distances. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation: Foundational Techniques. ISoLA 2016. Lecture Notes in Computer Science(), vol 9952. Springer, Cham. https://doi.org/10.1007/978-3-319-47166-2_3

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