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Monadic Second-Order Logic with Arbitrary Monadic Predicates

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Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8634))

Abstract

We study Monadic Second-Order Logic (MSO) over finite words, extended with (non-uniform arbitrary) monadic predicates. We show that it defines a class of languages that has algebraic, automata-theoretic and machine-independent characterizations. We consider the regularity question: given a language in this class, when is it regular? To answer this, we show a substitution property and the existence of a syntactical predicate.

We give three applications. The first two are to give simple proofs of the Straubing and Crane Beach Conjectures for monadic predicates, and the third is to show that it is decidable whether a language defined by an MSO formula with morphic predicates is regular.

The authors are supported by the project ANR 2010 BLAN 0202 02 (FREC). The first author is supported by the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement 259454 (GALE) and 239850 (SOSNA). The second author is supported by Fondation CFM.

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Author information

Authors and Affiliations

  1. LIAFA, Paris 7, France

    Nathanaël Fijalkow & Charles Paperman

  2. University of Warsaw, Poland

    Nathanaël Fijalkow

Authors
  1. Nathanaël Fijalkow
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  2. Charles Paperman
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Fijalkow, N., Paperman, C. (2014). Monadic Second-Order Logic with Arbitrary Monadic Predicates. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_24

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  • DOI: https://doi.org/10.1007/978-3-662-44522-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44521-1

  • Online ISBN: 978-3-662-44522-8

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