An automata theoretic decision procedure for the propositional mu-calculus
Information and Computation
Local model checking in the modal mu-calculus
TAPSOFT '89 2nd international joint conference on Theory and practice of software development
Theoretical Computer Science
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)
Modal and temporal properties of processes
Modal and temporal properties of processes
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
A Decision Procedure for the Propositional µ-Calculus
Proceedings of the Carnegie Mellon Workshop on Logic of Programs
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
The complexity of tree automata and logics of programs
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
The modal µ-calculus caught off guard
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
A Goal-Directed Decision Procedure for Hybrid PDL
Journal of Automated Reasoning
| Hi-index | 0.00 |
This paper presents a tableau system for determining satisfiability of modal μ -calculus formulas. The modal μ -calculus, which can be seen as an extension of modal logic with the least and greatest fixpoint operators, is a logic extensively studied in verification and has been shown to subsume many well-known temporal and modal logics including CTL, CTL*, and PDL. Concerning the satisfiability problem, the known methods in literature employ results from the theory of automata on infinite objects. The tableau system presented here provides an alternative solution which does not rely on automata theory. Since every tableau in the system is a finite tree structure (bounded by the size of the initial formula), this leads to a decision procedure for satisfiability and a small model property. The key features are the use of names to keep track of the unfolding of variables and the notion of name signatures used in the completeness proof.