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Polynomial-Time Alternating Probabilistic Bisimulation for Interval MDPs

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Book cover Dependable Software Engineering. Theories, Tools, and Applications (SETTA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10606))

Abstract

Interval Markov decision processes (IMDPs) extend classical MDPs by allowing intervals to be used as transition probabilities. They provide a powerful modelling tool for probabilistic systems with an additional variation or uncertainty that relaxes the need of knowing the exact transition probabilities, which are usually difficult to get from real systems. In this paper, we discuss a notion of alternating probabilistic bisimulation to reduce the size of the IMDPs while preserving the probabilistic CTL properties it satisfies from both computational complexity and compositional reasoning perspectives. Our alternating probabilistic bisimulation stands on the competitive way of resolving the IMDP nondeterminism which in turn finds applications in the settings of the controller (parameter) synthesis for uncertain (parallel) probabilistic systems. By using the theory of linear programming, we improve the complexity of computing the bisimulation from the previously known EXPTIME to PTIME. Moreover, we show that the bisimulation for IMDPs is a congruence with respect to two facets of parallelism, namely synchronous product and interleaving. We finally demonstrate the practical effectiveness of our proposed approaches by applying them on several case studies using a prototypical tool.

This work is supported by the ERC Advanced Investigators Grant 695614 (POWVER), by the CAS/SAFEA International Partnership Program for Creative Research Teams, by the National Natural Science Foundation of China (Grants No. 61550110506 and 61650410658), by the Chinese Academy of Sciences Fellowship for International Young Scientists, and by the CDZ project CAP (GZ 1023).

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Author information

Authors and Affiliations

  1. Saarland University, Saarland Informatics Campus, Saarbrücken, Germany

    Vahid Hashemi, Ernst Moritz Hahn & Holger Hermanns

  2. State Key Laboratory of Computer Science, ISCAS, Beijing, China

    Andrea Turrini & Ernst Moritz Hahn

  3. Masdar Institute of Science and Technology, Abu Dhabi, UAE

    Khaled Elbassioni

Authors
  1. Vahid Hashemi
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  2. Andrea Turrini
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  3. Ernst Moritz Hahn
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  4. Holger Hermanns
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  5. Khaled Elbassioni
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Correspondence to Vahid Hashemi .

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Editors and Affiliations

  1. Aalborg University, Aalborg, Denmark

    Kim Guldstrand Larsen

  2. University of Pennsylvania, Philadelphia, Pennsylvania, USA

    Oleg Sokolsky

  3. National University of Defense Technology, Changsha, China

    Ji Wang

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Hashemi, V., Turrini, A., Hahn, E.M., Hermanns, H., Elbassioni, K. (2017). Polynomial-Time Alternating Probabilistic Bisimulation for Interval MDPs. In: Larsen, K., Sokolsky, O., Wang, J. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2017. Lecture Notes in Computer Science(), vol 10606. Springer, Cham. https://doi.org/10.1007/978-3-319-69483-2_2

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