Building the minimal DFA for the set of all subwords of a word on-line in linear time

  • A. Blumer
  • J. Blumer
  • A. Ehrenfeucht
  • D. Haussler
  • R. McConnell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 172)


Let a partial deterministic finite automaton be a DFA in which each state need not have a transition edge for each letter of the alphabet. We demonstrate that the minimal partial DFA for the set of all subwords of a given word w, |w| > 2, has at most 2|w| − 2 states and 3|w| − 4 transition edges, independently of the alphabet size. We give an algorithm to build this minimal partial DFA from the input w on-line in linear time.


Equivalence Class String Match Transition Edge Deterministic Finite Automaton Longe Word 
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 1984

Authors and Affiliations

  • A. Blumer
    • 1
  • J. Blumer
    • 1
  • A. Ehrenfeucht
    • 1
  • D. Haussler
    • 1
  • R. McConnell
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of DenverDenver

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