An automata theoretic decision procedure for the propositional mu-calculus
Information and Computation
Handbook of theoretical computer science (vol. B)
CTL and ECTL as fragments of the modal &mgr;-calculus
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
The Complexity of Tree Automata and Logics of Programs
SIAM Journal on Computing
Completeness of Kozen's axiomatisation of the propositional &mgr;-calculus
Information and Computation
An automata-theoretic approach to branching-time model checking
Journal of the ACM (JACM)
The Propositional Mu-Calculus is Elementary
Proceedings of the 11th Colloquium on Automata, Languages and Programming
Local Model-Checking of Modal Mu-Calculus on Acyclic Labeled Transition Systems
TACAS '02 Proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Temporal Logic with Fixed Points
Temporal Logic in Specification
A Decision Procedure for the Propositional µ-Calculus
Proceedings of the Carnegie Mellon Workshop on Logic of Programs
Automata, Tableaux and Temporal Logics (Extended Abstract)
Proceedings of the Conference on Logic of Programs
From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A Tableau System for the Modal μ-Calculus
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Solving parity games in big steps
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
A Solver for Modal Fixpoint Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
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The modal µ-calculus extends basic modal logic with second-order quantification in terms of arbitrarily nested fixpoint operators. Its satisfiability problem is EXPTIME-complete. Decision procedures for the modal µ-calculus are not easy to obtain though since the arbitrary nesting of fixpoint constructs requires some combinatorial arguments for showing the well-foundedness of least fixpoint unfoldings. The tableau-based decision procedures so far also make assumptions on the unfoldings of fixpoint formulas, e.g. explicitly require formulas to be in guarded normal form. In this paper we present a tableau calculus for deciding satisfiability of arbitrary, i.e. not necessarily guarded µ-calculus formulas. The novel contribution is a new unfolding rule for greatest fixpoint formulas which shows how to handle unguardedness without an explicit transformation into guarded form, thus avoiding a (seemingly) exponential blow-up in formula size. We prove soundness and completeness of the calculus, and discuss its advantages over existing approaches.