Decidability and undecidability results on the modal µ-calculus with a natural number-valued semantics

Authors:
Alexis Goyet;Masami Hagiya;Yoshinori Tanabe
Affiliations:
Ecole Normale Supérieure;University of Tokyo;National Institute of Informatics, Japan
Venue:
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
Year:
2010

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Abstract

In our previous study, we defined a semantics of modal µ-calculus based on min-plus algebra N∞ and developed a model-checking algorithm. N∞ is the set of all natural numbers and infinity (∞), and has two operations min and plus. In our semantics, disjunctions are interpreted by min and conjunctions by plus. This semantics allows interesting properties of a Kripke structure to be expressed using simple formulae. In this study, we investigate the satisfiability problem in the N∞ semantics and show decidability and undecidability results: the problem is decidable if the logic does not contain the implication operator, while it becomes undecidable if we allow the implication operator.