Characterizing EF over Infinite Trees and Modal Logic on Transitive Graphs

  • Balder ten Cate
  • Alessandro Facchini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6907)

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.

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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2011

Authors and Affiliations

  • Balder ten Cate
    • 1
  • Alessandro Facchini
    • 2
  1. 1.University of CaliforniaSanta CruzUSA
  2. 2.Warsaw UniversityPoland

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