Bisimulation Invariant Monadic-Second Order Logic in the Finite

Authors Achim Blumensath, Felix Wolf

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Achim Blumensath
  • Masaryk University Brno
Felix Wolf
  • Technische Universität Darmstadt, Institute TEMF, Graduate School of Excellence Computational Engineering

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Achim Blumensath and Felix Wolf. Bisimulation Invariant Monadic-Second Order Logic in the Finite. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 117:1-117:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the modal mu-calculus. Using these characterisations we prove for some simple classes of transition systems that this is indeed the case. In particular, we show that, over the class of all finite transition systems with Cantor-Bendixson rank at most k, bisimulation-invariant MSO coincides with L_mu.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
  • bisimulation
  • monadic second-order logic
  • composition method


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