Characterizing EF over infinite trees and modal logic on transitive graphs

Authors:
Balder ten Cate;Alessandro Facchini
Affiliations:
University of California, Santa Cruz;Warsaw University
Venue:
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Year:
2011

Citing 11
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Abstract

We provide several effective equivalent characterizations of EF (the modal logic of the descendant relation) on arbitrary trees. More specifically, we prove that, for EF-bisimulation invariant properties of trees, being definable by an EF formula, being a Borel set, and being definable in weak monadic second order logic, all coincide. The proof builds upon a known algebraic characterization of EF for the case of finitely branching trees due to Bojańczyk and Idziaszek. We furthermore obtain characterizations of modal logic on transitive Kripke structures as a fragment of weak monadic second order logic and of the µ-calculus.