A rewriting of Fife's theorem about overlap-free words

  • J. Berstel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 812)


The purpose of this expository paper is to present a self-contained proof of a famous theorem of Fife that gives a full description of the set of infinite overlap-free words over a binary alphabet. Fife's characterization consists in a parameterization of these infinite words by a set of infinite words over a ternary alphabet. The result is that the latter is a regular set. The proof is by the explicit construction of the minimal automaton, obtained by the method of left quotients.


Finite Automaton Canonical Decomposition Binary Word Formal Language Theory Infinite Word 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • J. Berstel
    • 1
  1. 1.LITP, Institut Blaise PascalUniversité Pierre et Marie CurieParis Cedex 05

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