A decision procedure for the alternation-free two-way modal µ-calculus

Authors:
Yoshinori Tanabe;Koichi Takahashi;Mitsuharu Yamamoto;Akihiko Tozawa;Masami Hagiya
Affiliations:
CREST, Japan Science and Technology Agency;Research Center for Verification and Semantics, National Institute of Advanced Industrial Science and Technology (AIST);Faculty of Science, Chiba University;Tokyo Research Laboratory, IBM Japan ltd., IBM Research, Japan;Graduate School of Information Science and Technology, University of Tokyo
Venue:
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Year:
2005

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Abstract

The satisfiability checking problem is known to be decidable for a variety of modal/temporal logics such as the modal μ-calculus, but effective implementation has not necessarily been developed for all such logics. In this paper, we propose a decision procedure using the tableau method for the alternation-free two-way modal μ-calculus. Although the size of the tableau set maintained in the method might be large for complex formulas, the set and the operations on it can be expressed using BDD and therefore we can implement the method in an effective way.