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Bisimulation Invariant Monadic-Second Order Logic in the Finite

Authors Achim Blumensath, Felix Wolf

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Author Details

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

Funding

  • Blumensath, Achim: Work supported by the Czech Science Foundation, grant No. GA17-01035S
  • Wolf, Felix: Work partially supported by the \emph{Excellence Initiative} of the German Federal and State Governments and the Graduate School of Computational Engineering at Technische Universität Darmstadt

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.ICALP.2018.117

Abstract

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
Keywords
  • bisimulation
  • monadic second-order logic
  • composition method

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