Translating regular expressions into small ε-free nondeterministic finite automata

  • Juraj Hromkovič
  • Sebastian Seibert
  • Thomas Wilke
Automata Theory I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1200)


It is proved that every regular expression of size n can be converted into an equivalent nondeterministic finite automaton (NFA) of size O(n(log n)2) in polynomial time. The best previous conversions result in NFAs of worst case size Θ(n2). Moreover, the nonexistence of any linear conversion is proved: we give a language L n described by a regular expression of size O(n) such that every NFA accepting L n is of size Ω(n log n).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  • Sebastian Seibert
    • 1
  • Thomas Wilke
    • 1
  1. 1.Institut für Informatik und Praktische MathematikChristian-Albrechts-Universität zu KielKielGermany

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