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Bounded game-theoretic semantics for modal mu-calculus
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A new game-theoretic semantics (GTS) for the modal mu-calculus is introduced that 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.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.read more
Citations
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Journal ArticleDOI
Formula size games for modal logic and μ-calculus
Lauri Hella,Miikka Vilander +1 more
TL;DR: A new version of formula size game for modal logic that characterizes the equivalence of pointed Kripke-models up to formulas of given numbers of modal operators and binary connectives is proposed.
Journal ArticleDOI
Game-Theoretic Semantics for ATL+ with Applications to Model Checking
TL;DR: In this paper, a game-theoretic semantics for the fragment AT L + of the alternating-time temporal logic AT L ⁎ was proposed, which is equivalent to the standard compositional semantics of AT L+ with perfect-recall strategies.
Journal ArticleDOI
Bounded Game-Theoretic Semantics for Modal Mu-Calculus and Some Variants
TL;DR: In this paper, a game-theoretic semantics (GTS) for the modal mu-calculus is introduced, which 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.
Journal ArticleDOI
Alternating-time temporal logic ATL with finitely bounded semantics
TL;DR: It is shown that the finitary tableau system provides an exponential-time decision procedure for the satisfiability problem of ATL FB and thus establishes its EXPTIME-completeness and an infinitary axiomatization for ATL FB is presented and proved soundness and completeness.
Journal ArticleDOI
Game-Theoretic Semantics for Alternating-Time Temporal Logic
TL;DR: It is shown that, in bounded GTS, truth of ATL formulae can always be determined in finite time, that is, without constructing infinite paths.
References
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Symbolic Model Checking without BDDs
TL;DR: This paper shows how boolean decision procedures, like Stalmarck's Method or the Davis & Putnam Procedure, can replace BDDs, and introduces a bounded model checking procedure for LTL which reduces model checking to propositional satisfiability.
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Results on the propositional μ-calculus
TL;DR: A propositional μ-calculus L μ is defined and study, which consists essentially of propositional modal logic with a least fixpoint operator that is syntactically simpler yet strictly more expressive than Propositional Dynamic Logic (PDL).
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Modal Mu-Calculi
TL;DR: In this chapter, least and greatest solutions to recursive modal equations were represented using the fixed point quantifiers μZ and υZ and the connectives to modal logic are added, thereby providing a very rich temporal logic.
Journal Article
Bounded Model Checking for the Universal Fragment of CTL
TL;DR: The concept of bounded model checking can be extended to ACTL (the universal fragment of CTL) and the implementation of the algorithm for Elementary Net Systems is described together with the experimental results.
Journal ArticleDOI
Finitary fairness
Rajeev Alur,Thomas A. Henzinger +1 more
TL;DR: It is argued that the standard definition of fairness often is unnecessarily weak and can be replaced by the stronger, yet still abstract, notion of finitary fairness, which solves the fundamental problem of consensus in a faulty asynchronous distributed environment.