Computing ε-free NFA from regular expressions in O(n log2(N)) time

  • Christian Hagenah
  • Anca Muscholl
Contributed Papers Automata and Transducers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)


The standard procedure to transform a regular expression to an ε-free NFA yields a quadratic blow-up of the number of transitions. For a long time this was viewed as an unavoidable fact. Recently Hromkovič [5] exhibited a construction yielding ε-free NFA with O(n log2(n)) transitions. A rough estimation of the time needed for their construction shows a cubic time bound. The known lower bound is Ω(n log(n)). In this paper we present a sequential algorithm for the construction described in [5] which works in time O(n log(n) + size of the output). On a CREW PRAM the construction is possible in time O(log(n)) using O(n + (size of the output)/log(n)) processors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Christian Hagenah
    • 1
  • Anca Muscholl
    • 1
  1. 1.Institut für InformatikUniversität StuttgartStuttgartGermany

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