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An Efficient Synthesis Algorithm for Parametric Markov Chains Against Linear Time Properties

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Dependable Software Engineering: Theories, Tools, and Applications (SETTA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9984))

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Abstract

In this paper, we propose an efficient algorithm for the parameter synthesis of PLTL formulas with respect to parametric Markov chains. The PLTL formula is translated to an almost fully partitioned Büchi automaton which is then composed with the parametric Markov chain. We then reduce the problem to solving an optimisation problem, allowing to decide the satisfaction of the formula using an SMT solver. The algorithm works also for interval Markov chains. The complexity is linear in the size of the Markov chain, and exponential in the size of the formula. We provide a prototype and show the efficiency of our approach on a number of benchmarks.

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Acknowledgement

This work is supported by the CDZ project CAP (GZ 1023), by the Chinese Academy of Sciences Fellowship for International Young Scientists, by the National Natural Science Foundation of China (Grants No. 61532019, 61472473, 61550110249, 61550110506, 61103012, 61379054, and 61272335), and by the CAS/SAFEA International Partnership Program for Creative Research Teams.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, CAS, Beijing, China

    Yong Li, Andrea Turrini, Ernst Moritz Hahn & Lijun Zhang

  2. University of Chinese Academy of Sciences, Beijing, China

    Yong Li & Lijun Zhang

  3. College of Computer Science, National University of Defense Technology, Changsha, China

    Wanwei Liu

Authors
  1. Yong Li
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  2. Wanwei Liu
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  3. Andrea Turrini
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  4. Ernst Moritz Hahn
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Correspondence to Andrea Turrini .

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Editors and Affiliations

  1. Carl von Ossietzky Universität, Oldenburg, Germany

    Martin Fränzle

  2. University of New Mexico, Albuquerque, New Mexico, USA

    Deepak Kapur

  3. Chinese Academy of Sciences, Beijing, China

    Naijun Zhan

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Li, Y., Liu, W., Turrini, A., Hahn, E.M., Zhang, L. (2016). An Efficient Synthesis Algorithm for Parametric Markov Chains Against Linear Time Properties. In: Fränzle, M., Kapur, D., Zhan, N. (eds) Dependable Software Engineering: Theories, Tools, and Applications. SETTA 2016. Lecture Notes in Computer Science(), vol 9984. Springer, Cham. https://doi.org/10.1007/978-3-319-47677-3_18

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  • DOI: https://doi.org/10.1007/978-3-319-47677-3_18

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