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Compositional Solution of Mean Payoff Games by String Diagrams

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Principles of Verification: Cycling the Probabilistic Landscape

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15262))

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Abstract

Following our recent development of a compositional model checking algorithm for Markov decision processes, we present a compositional framework for solving mean payoff games (MPGs). The framework is derived from category theory: MPGs (extended with open ends) get composed in so-called string diagrams and thus organized in a monoidal category; their solution is then expressed as a functor, whose preservation properties embody compositionality. The key question to compositionality is how to enrich the semantic domain; the categorical framework gives an informed guidance in solving the question by singling out the algebraic structure required in the extended semantic domain. We implemented our compositional solution in Haskell; depending on benchmarks, it can outperform an existing algorithm by an order of magnitude.

We thank to Massimo Benerecetti, Daniele Dell’Erba, and Fabio Mogavero for kindly sharing their implementation. We thank the reviewers for the previous versions of the paper for their useful comments. K.W., C.E., and I.H. are supported by ERATO HASUO Metamathematics for Systems Design Project (No. JPMJER1603) and the ASPIRE grant No. JPMJAP2301, JST. K.W. is supported by the JST grants No. JPMJFS2136 and JPMJAX23CU.

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Notes

  1. 1.

    it is available at https://github.com/Kazuuuuuki/compMPG.

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Correspondence to Kazuki Watanabe .

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To Joost-Pieter Katoen on his 60th birthday. This paper comes from our recent endeavor to use the language of category theory for a general account of, and efficient algorithms for, model checking. In this endeavor, the beautiful theory of probabilistic model checking developed by Joost-Pieter and his coauthors has been the main source of inspiration. Comparing the theory with the conventional (non-probabilistic) model checking, we have learned what theoretical constructs are essential and thus amenable to categorical abstraction. We have also been thrilled to work with the gang of (former and present) students of Joost-Pieter—they are not only excellent researchers but also have open and fun-loving minds. We thus dedicate this paper to Joost-Pieter’s heritage, in scientific work and in people.

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Watanabe, K., Eberhart, C., Asada, K., Hasuo, I. (2025). Compositional Solution of Mean Payoff Games by String Diagrams. In: Jansen, N., et al. Principles of Verification: Cycling the Probabilistic Landscape . Lecture Notes in Computer Science, vol 15262. Springer, Cham. https://doi.org/10.1007/978-3-031-75778-5_20

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