On Modal μ-Calculus in S5 and Applications

Authors:
Giovanna D'Agostino;Giacomo Lenzi
Affiliations:
Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, 33100 Udine, Italy. giovanna.dagostino@uniud.it;Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte Don Melillo 1, 84084 Fisciano SA, Italy. gilenzi@unisa.it
Venue:
Fundamenta Informaticae - Special Issue on the Italian Conference on Computational Logic: CILC 2011
Year:
2013

Citing 7
Cited 0

Tree automata, Mu-Calculus and determinacy

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Deciding the winner in parity games is in UP ∩ co-UP

Information Processing Letters
Model checking

Model checking
Reasoning About Knowledge

Reasoning About Knowledge
On the universal and existential fragments of the μ-calculus

Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2003)
Sequent Calculi for the Modal µ-Calculus over S5

Journal of Logic and Computation
On the μ-calculus over transitive and finite transitive frames

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the μ-calculus over graphs where the accessibility relation is an equivalence S5-graphs. We show that the vectorial μ-calculus model checking problem over arbitrary graphs reduces to the vectorial, existential μ-calculus model checking problem over S5 graphs. Moreover, we give a proof that satisfiability of μ-calculus in S5 is NP-complete, and by using S5 graphs we give a new proof that the satisfiability problem of the existential μ-calculus is also NP-complete. Finally we prove that on multimodal S5, in contrast with the monomodal case, the fixpoint hierarchy of the μ-calculus is infinite and the finite model property fails.