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The Membership Problem for Regular Expressions with Unordered Concatenation and Numerical Constraints

  • Conference paper
Language and Automata Theory and Applications (LATA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7183))

Abstract

We study the membership problem for regular expressions extended with operators for unordered concatenation and numerical constraints. The unordered concatenation of a set of regular expressions denotes all sequences consisting of exactly one word denoted by each of the expressions. Numerical constraints are an extension of regular expressions used in many applications, e.g. text search (e.g., UNIX grep), document formats (e.g. XML Schema). Regular expressions with unordered concatenation and numerical constraints denote the same languages as the classical regular expressions, but, in certain important cases, exponentially more succinct. We show that the membership problem for regular expressions with unordered concatenation (without numerical constraints) is already NP-hard. We show a polynomial-time algorithm for the membership problem for regular expressions with numerical constraints and unordered concatenation, when restricted to a subclass called strongly 1-unambiguous.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Oslo, Norway

    Dag Hovland

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  1. Dag Hovland
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Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

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Hovland, D. (2012). The Membership Problem for Regular Expressions with Unordered Concatenation and Numerical Constraints. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_27

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  • DOI: https://doi.org/10.1007/978-3-642-28332-1_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28331-4

  • Online ISBN: 978-3-642-28332-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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