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arXiv · 1706.00753

Bounded game-theoretic semantics for modal mu-calculus

Lauri Hella·Antti Kuusisto·Raine Rönnholm
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Abstract

We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the considered transition system is infinite. The novel games offer alternative approaches to various constructions in the framework of the mu-calculus. For example, they have already been successfully used as a basis for an approach leading to a natural formula size game for the logic. While our main focus is introducing the new GTS, we also consider some applications to demonstrate its uses. For example, we consider a natural model transformation procedure that reduces model checking games to checking a single, fixed formula in the constructed models, and we also use the GTS to identify new alternative variants of the mu-calculus with PTime model checking.

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Lauri Hella, Antti Kuusisto, Raine Rönnholm. 2017-06-02. Bounded game-theoretic semantics for modal mu-calculus. https://arxiv.org/abs/1706.00753

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