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.

中文翻译：

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模态 Mu 演算和一些变体的有界博弈论语义

我们为模态 mu 演算引入了一种新的博弈论语义（GTS）。我们所谓的有界 GTS 用仅出现有限路径的替代评估游戏取代了奇偶游戏；即使考虑的过渡系统是无限的，也不需要无限路径。新游戏为 mu 演算框架中的各种构造提供了替代方法。例如，它们已经成功地用作导致逻辑的自然公式大小游戏的方法的基础。虽然我们的主要重点是介绍新的 GTS，但我们也考虑了一些应用程序来演示其用途。例如，我们考虑一个自然模型转换过程，将模型检查游戏简化为检查构建模型中的单个固定公式，