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Categories and Types in Logic, Language, and Physics pp 51–62Cite as

NP-Completeness of Grammars Based Upon Products of Free Pregroups

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8222))

Abstract

Pregroup grammars are context-free lexicalized grammars based upon free pregroups which can describe parts of the syntax of natural languages. Some extensions are useful to model special constructions like agreements with complex features or non-projective relations or dependencies. A simple solution for these problems is given by lexicalized grammars based upon the product of free pregroups rather than on a single free pregroup. Such grammars are not necessarily context-free. However, the membership problem is NP-complete. To prove this theorem, the article defines a particular grammar built on the product of three free pregroups. This grammar is used to encode any SAT problem as a membership problem in the language corresponding to the grammar.

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Author information

Authors and Affiliations

  1. LINA - UMR 6241, Université de Nantes & CNRS, 2, rue de la Houssiniére, BP 92208, 44322, Nantes Cedex 03, France

    Denis Béchet

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  1. Denis Béchet
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Editors and Affiliations

  1. Department of Philosophy, Education and Quantitative Economics, Gabriele D’Annunzio University, Chieti-Pescara, Via dei Vestini 31, 60100, Chieti, Italy

    Claudia Casadio

  2. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Bob Coecke

  3. Utrecht Institute of Linguistics OTS, Utrecht University, Trans 10,, 3512 JK, Utrecht, The Netherlands

    Michael Moortgat

  4. Department of Mathematics, University of Ottawa, 585 King Edward, K1N 6N5, Ottawa, ON, Canada

    Philip Scott

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Béchet, D. (2014). NP-Completeness of Grammars Based Upon Products of Free Pregroups. In: Casadio, C., Coecke, B., Moortgat, M., Scott, P. (eds) Categories and Types in Logic, Language, and Physics. Lecture Notes in Computer Science, vol 8222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54789-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-54789-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54788-1

  • Online ISBN: 978-3-642-54789-8

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