Bounded game-theoretic semantics for modal mu-calculus

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. 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. We also use the GTS to identify new alternative variants of the mu-calculus, including close variants of the logic with PTime model checking; variants with iteration limited to finite ordinals; and other systems where the semantic or syntactic specification of the mu-calculus has been modified in a natural way suggested by the GTS.