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A Note on Multidimensional Dyck Languages

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Categories and Types in Logic, Language, and Physics

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

Abstract

Multidimensional Dyck languages generalize the language of balanced brackets to alphabets of size > 2. Words contain each alphabet symbol with the same multiplicity. In addition, reading a word from left to right, there are always at least as many a i as a(i + 1), where a j is the jth alphabet symbol in the lexicographic ordering.

We compare the Dyck languages with MIX languages, where the multiplicity constraint is respected, but the order of the symbols is free. To understand the combinatorics of the Dyck languages, we study the bijection with standard Young tableaux of rectangular shape, and, for the three-dimensional case, with planar webs for combinatorial spider categories. We present a typelogical analysis of Dyck languages with an alphabet of size d in terms of a construction that aligns (d − 1) grammars for the two-symbol case.

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Authors and Affiliations

  1. Utrecht Institute of Linguistics, The Netherlands

    Michael Moortgat

Authors
  1. Michael Moortgat
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Editor information

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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Moortgat, M. (2014). A Note on Multidimensional Dyck Languages. 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_16

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  • DOI: https://doi.org/10.1007/978-3-642-54789-8_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54788-1

  • Online ISBN: 978-3-642-54789-8

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