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Capturing MSO with One Quantifier

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Book cover Fields of Logic and Computation II

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9300))

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Abstract

We construct a single Lindström quantifier Q such that \(\text {FO} (Q)\), the extension of first-order logic with Q has the same expressive power as monadic second-order logic on the class of binary trees (with distinct left and right successors) and also on unranked trees with a sibling order. This resolves a conjecture by ten Cate and Segoufin. The quantifier Q is a variation of a quantifier expressing the Boolean satisfiability problem.

The research reported here was carried out while the first author was a visitor at ENS Cachan, funded by a Leverhulme Trust Study Abroad Fellowship.

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Notes

  1. 1.

    As written in [9], the question asks for a set of such quantifiers with expressive power equivalent to \(\text {FO} (\text {MTC}) \). This is clearly a typographical error and \(\text {MSO} \) is what is meant.

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Author information

Authors and Affiliations

  1. University of Cambridge Computer Laboratory, Cambridge, UK

    Anuj Dawar

  2. INRIA and ENS Cachan, Cachan, France

    Luc Segoufin

Authors
  1. Anuj Dawar
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  2. Luc Segoufin
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Corresponding author

Correspondence to Anuj Dawar .

Editor information

Editors and Affiliations

  1. Steklov Mathematical Institute, Moscow, Russia

    Lev D. Beklemishev

  2. University of Michigan, Ann Arbor, Michigan, USA

    Andreas Blass

  3. Tel Aviv University, Tel Aviv, Israel

    Nachum Dershowitz

  4. Universität des Saarlandes, Saarbrücken, Germany

    Bernd Finkbeiner

  5. Microsoft Research, REDMOND, Washington, USA

    Wolfram Schulte

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Dawar, A., Segoufin, L. (2015). Capturing MSO with One Quantifier. In: Beklemishev, L., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds) Fields of Logic and Computation II. Lecture Notes in Computer Science(), vol 9300. Springer, Cham. https://doi.org/10.1007/978-3-319-23534-9_8

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  • DOI: https://doi.org/10.1007/978-3-319-23534-9_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23533-2

  • Online ISBN: 978-3-319-23534-9

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