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Baire Category Quantifier in Monadic Second Order Logic

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Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9135))

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Abstract

We consider Rabin’s Monadic Second Order logic (MSO) of the full binary tree extended with Harvey Friedman’s “for almost all” second-order quantifier (\(\forall ^*\)) with semantics given in terms of Baire Category. In Theorem 1 we prove that the new quantifier can be eliminated (\(\text {MSO}\!+\!\forall ^* \!=\! \text {MSO}\)). We then apply this result to prove in Theorem 2 that the finite–SAT problem for the qualitative fragment of the probabilistic temporal logic pCTL* is decidable. This extends a previous result of Brázdil, Forejt, Křetínský and Kučera valid for qualitative pCTL.

H. Michalewski—Author supported by Polands National Science Centre grant no. 2014-13/B/ST6/03595.

M. Mio—Author supported by grant “Projet Émergent PMSO” of the École Normale Supérieure de Lyon.

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Author information

Authors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Henryk Michalewski

  2. CNRS/ENS-Lyon, Lyon, France

    Matteo Mio

Authors
  1. Henryk Michalewski
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  2. Matteo Mio
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Correspondence to Matteo Mio .

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Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Michalewski, H., Mio, M. (2015). Baire Category Quantifier in Monadic Second Order Logic. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_29

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  • DOI: https://doi.org/10.1007/978-3-662-47666-6_29

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  • Print ISBN: 978-3-662-47665-9

  • Online ISBN: 978-3-662-47666-6

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