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International Conference on Developments in Language Theory

DLT 2017: Developments in Language Theory pp 260–271Cite as

Two-Variable First Order Logic with Counting Quantifiers: Complexity Results

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10396))

Abstract

Etessami et al. [5] showed that satisfiability of two-variable first order logic \(\mathrm {FO}^2\)[<] on word models is Nexptime-complete. We extend this upper bound to the slightly stronger logic \(\mathrm {FO}^2\)[\(<,succ ,\equiv \)], which allows checking whether a word position is congruent to r modulo q, for some divisor q and remainder r. If we allow the more powerful modulo counting quantifiers of Straubing, Thérien et al. [22] (we call this two-variable fragment FOmod \(^2\)[\(<,succ \)]), satisfiability becomes Expspace-complete. A more general counting quantifier, FOunC\(^2\)[\(<,succ \)], makes the logic undecidable.

Affiliated to Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094.

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Acknowledgments

We would like to thank four DLT referees and the DLT program committee for their suggestions to improve this paper.

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Authors and Affiliations

  1. The Institute of Mathematical Sciences, CIT Campus, Chennai, 600113, India

    Kamal Lodaya

  2. Chennai Mathematical Institute, Siruseri, Kelambakkam, 603103, India

    A. V. Sreejith

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  1. Kamal Lodaya
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  2. A. V. Sreejith
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Correspondence to A. V. Sreejith .

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Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Émilie Charlier

  2. Université de Liège, Liège, Belgium

    Julien Leroy

  3. Université de Liège, Liège, Belgium

    Michel Rigo

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Lodaya, K., Sreejith, A.V. (2017). Two-Variable First Order Logic with Counting Quantifiers: Complexity Results. In: Charlier, É., Leroy, J., Rigo, M. (eds) Developments in Language Theory. DLT 2017. Lecture Notes in Computer Science(), vol 10396. Springer, Cham. https://doi.org/10.1007/978-3-319-62809-7_19

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  • DOI: https://doi.org/10.1007/978-3-319-62809-7_19

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  • Print ISBN: 978-3-319-62808-0

  • Online ISBN: 978-3-319-62809-7

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