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International Symposium on Mathematical Foundations of Computer Science

MFCS 2009: Mathematical Foundations of Computer Science 2009 pp 369–381Cite as

Regular Expressions with Counting: Weak versus Strong Determinism

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5734))

Abstract

We study deterministic regular expressions extended with the counting operator. There exist two notions of determinism, strong and weak determinism, which almost coincide for standard regular expressions. This, however, changes dramatically in the presence of counting. In particular, we show that weakly deterministic expressions with counting are exponentially more succinct and strictly more expressive than strongly deterministic ones, even though they still do not capture all regular languages. In addition, we present a finite automaton model with counters, study its properties and investigate the natural extension of the Glushkov construction translating expressions with counting into such counting automata. This translation yields a deterministic automaton if and only if the expression is strongly deterministic. These results then also allow to derive upper bounds for decision problems for strongly deterministic expressions with counting.

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Author information

Authors and Affiliations

  1. School for Information Technology, Hasselt University and Transnational University of Limburg, Belgium

    Wouter Gelade & Marc Gyssens

  2. Technical University of Dortmund, Germany

    Wim Martens

Authors
  1. Wouter Gelade
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  2. Marc Gyssens
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  3. Wim Martens
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, Research partially funded by grant APVV 0433-06, Bratislava, Slovakia

    Rastislav Královič

  2. Members of EACSL Jury for the Ackermann Award, Poland

    Damian Niwiński

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© 2009 Springer-Verlag Berlin Heidelberg

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Gelade, W., Gyssens, M., Martens, W. (2009). Regular Expressions with Counting: Weak versus Strong Determinism. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_32

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  • DOI: https://doi.org/10.1007/978-3-642-03816-7_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03815-0

  • Online ISBN: 978-3-642-03816-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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