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arXiv · 2307.08034

Compositional Solution of Mean Payoff Games by String Diagrams

Kazuki Watanabe·Clovis Eberhart·Kazuyuki Asada·Ichiro Hasuo
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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, specifically that of monoidal categories: 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. As usual, 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.

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Kazuki Watanabe, Clovis Eberhart, Kazuyuki Asada, Ichiro Hasuo. 2023-07-16. Compositional Solution of Mean Payoff Games by String Diagrams. https://arxiv.org/abs/2307.08034

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