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

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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)
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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References

  1. H. Andréka, J. van Benthem, and I. Németi. Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic, 27:217-274, 1998. Google Scholar
  2. J. van Benthem. Modal Correspondence Theory. Ph. D. Thesis, University of Amsterdam, Amsterdam, 1976. Google Scholar
  3. A. Blumensath, T. Colcombet, and C. Löding. Logical Theories and Compatible Operations. In J. Flum, E. Grädel, and T. Wilke, editors, Logic and Automata: History and Perspectives, pages 73-106. Amsterdam University Press, 2007. Google Scholar
  4. F. Carreiro. Fragments of Fixpoint Logics. PhD Thesis, Institute for Logic, Language and Computation, Amsterdam, 2015. Google Scholar
  5. I. Ciardelli and M. Otto. Bisimulation in Inquisitive Modal Logic. In Proc. 16th Conference on Theoretical Aspects of Rationality and Knowledge, erTARK 2017, pages 151-166, 2017. Google Scholar
  6. A. Dawar and D. Janin. On the bisimulation invariant fragment of monadic Σ₁ in the finite. In Proc. of the 24th Int. Conf. on Foundations of Software Technology and Theoretical Computer Science, erFSTTCS 2004, pages 224-236, 2004. Google Scholar
  7. E. Grädel, C. Hirsch, and M. Otto. Back and Forth Between Guarded and Modal Logics. ACM Transactions on Computational Logics, pages 418-463, 2002. Google Scholar
  8. E. Grädel, W. Thomas, and T. Wilke. Automata, Logic, and Infinite Games. erLNCS 2500. Springer-Verlag, 2002. Google Scholar
  9. C. Hirsch. Guarded Logics: Algorithms and Bisimulation. Ph. D. Thesis, erRWTH Aachen, Aachen, 2002. Google Scholar
  10. D. Janin and I. Walukiewicz. On the expressive completeness of the propositional mu-calculus with respect to monadic second order logic. In Proc. of the 7th International Conference on Concurrency Theory, erCONCUR 1996, pages 263-277, 1996. Google Scholar
  11. J. A. Makowsky. Algorithmic aspects of the Feferman-Vaught Theorem. Annals of Pure and Applied Logic, 126:159-213, 2004. Google Scholar
  12. F. Moller and A. Rabinovitch. On the expressive power of CTL*. In Proc. 14th erIEEE Symp. on Logic in Computer Science, erLICS, pages 360-369, 1999. Google Scholar
  13. F. Moller and A. Rabinovitch. Counting on CTL*: on the expressive power of monadic path logic. Information and Computation, 184:147-159, 2003. Google Scholar
  14. D. Perrin and J.-É. Pin. Infinite Words - Automata, Semigroups, Logic and Games. Elsevier, 2004. Google Scholar
  15. E. Rosen. Modal logic over finite structures. Journal of Logic, Language and Information, 6:427-439, 1997. Google Scholar
  16. S. Shelah. The Monadic Second Order Theory of Order. Annals of Mathematics, 102:379-419, 1975. Google Scholar
  17. C. Stirling. Bisimulation and logic. In D. Sangiorgi and J. Rutten, editors, Advanced topics in Bisimulation and Coinduction, pages 172-196. Cambridge University Press, 2011. Google Scholar
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