Regular Expressions with Counting: Weak versus Strong Determinism

  • Wouter Gelade
  • Marc Gyssens
  • Wim Martens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5734)


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.


Regular Expression Regular Language Parse Tree Counter Variable Counting Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Wouter Gelade
    • 1
  • Marc Gyssens
    • 1
  • Wim Martens
    • 2
  1. 1.School for Information TechnologyHasselt University and Transnational University of LimburgBelgium
  2. 2.Technical University of DortmundGermany

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