Minimal forbidden words and factor automata

  • M. Crochemore
  • F. Mignosi
  • A. Restivo
Contributed Papers Combinatorics on Words
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1450)


Let L(M) be the (factorial) language avoiding a given anti-factorial language M. We design an automaton accepting L(M) and built from the language M. The construction is effective if M is finite.

If M is the set of minimal forbidden words of a single word v, the automaton turns out to be the factor automaton of v (the minimal automaton accepting the set of factors of v).

We also give an algorithm that builds the trie of M from the factor automaton of a single word. It yields a non-trivial upper bound on the number of minimal forbidden words of a word.


factorial language anti-factorial language factor code factor automaton forbidden word avoiding a word failure function 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • M. Crochemore
    • 1
  • F. Mignosi
    • 2
  • A. Restivo
    • 2
  1. 1.Institut Gaspard-MongeFrance
  2. 2.Università di PalermoItaly

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