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Verification of Multiplayer Stochastic Games via Abstract Dependency Graphs

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Book cover Logic-Based Program Synthesis and Transformation (LOPSTR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12561))

Abstract

We design and implement an efficient model checking algorithm for alternating-time temporal logic (ATL) on turn-based multiplayer stochastic games with weighted transitions. This logic allows us to query about the existence of multiplayer strategies that aim to maximize the probability of game runs satisfying resource-bounded next and until logical operators, while requiring that the accumulated weight along the successful runs does not exceed a given upper bound. Our method relies on a recently introduced formalism of abstract dependency graphs (ADG) and we provide an efficient reduction of our model checking problem to finding the minimum fixed-point assignment on an ADG over the domain of unit intervals extended with certain-zero optimization. As the fixed-point computation on ADGs is performed in an on-the-fly manner without the need of a priori generating the whole graph, we achieve a performance that is comparable with state-of-the-art model checker PRISM-games for finding the exact solutions and sometimes an order of magnitude faster for queries that ask about approximate probability bounds. We document this on a series of scalable experiments from the PRISM-games benchmark that we annotate with weight information.

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Authors and Affiliations

  1. Department of Computer Science, Aalborg University, Selma Lagerlöfs Vej 300, 9220, Aalborg East, Denmark

    Søren Enevoldsen, Mathias Claus Jensen, Kim Guldstrand Larsen, Anders Mariegaard & Jiří Srba

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  1. Søren Enevoldsen
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  2. Mathias Claus Jensen
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  3. Kim Guldstrand Larsen
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  4. Anders Mariegaard
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  5. Jiří Srba
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Correspondence to Anders Mariegaard .

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  1. King’s College London, London, UK

    Maribel Fernández

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Enevoldsen, S., Jensen, M.C., Larsen, K.G., Mariegaard, A., Srba, J. (2021). Verification of Multiplayer Stochastic Games via Abstract Dependency Graphs. In: Fernández, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2020. Lecture Notes in Computer Science(), vol 12561. Springer, Cham. https://doi.org/10.1007/978-3-030-68446-4_13

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  • DOI: https://doi.org/10.1007/978-3-030-68446-4_13

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