论文信息 - A Rewriting of Fife's Theorem about Overlap-Free Words

A Rewriting of Fife's Theorem about Overlap-Free Words

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.

Jean Berstel | J. Berstel

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