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International Conference on Formal Modeling and Analysis of Timed Systems

FORMATS 2008: Formal Modeling and Analysis of Timed Systems pp 203–217Cite as

Model Checking HML on Piecewise-Constant Inhomogeneous Markov Chains

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5215))

Abstract

This paper presents a stochastic variant of Hennessy-Milner logic that is interpreted over (state-labeled) inhomogeneous continuous-time Markov chains (ICTMCs), i.e., Markov chains in which transition rates are functions over time t. For piecewise constant rate functions, the model-checking problem is shown to be reducible to finding the zeros of an exponential polynomial. Using Sturm sequences and Newton’s method, we obtain an approximative model-checking algorithm which is linear in the size of the ICTMC, logarithmic in the number of bits precision, and exponential in the nesting depth of the formula.

This research has taken place as part of the Research Training Group 1298 ALGOSYN funded by the German Research Council.

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Authors and Affiliations

  1. Software Modeling and Verification, RWTH Aachen University, Germany

    Joost-Pieter Katoen & Alexandru Mereacre

Authors
  1. Joost-Pieter Katoen
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  2. Alexandru Mereacre
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Franck Cassez Claude Jard

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Katoen, JP., Mereacre, A. (2008). Model Checking HML on Piecewise-Constant Inhomogeneous Markov Chains. In: Cassez, F., Jard, C. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2008. Lecture Notes in Computer Science, vol 5215. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85778-5_15

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  • DOI: https://doi.org/10.1007/978-3-540-85778-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85777-8

  • Online ISBN: 978-3-540-85778-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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