Fife's theorem revisited

Authors:
Jeffrey Shallit
Affiliations:
University of Waterloo, Waterloo, ON, Canada
Venue:
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Year:
2011

Citing 7
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Abstract

We give another proof of a theorem of Fife -- understood broadly as providing a finite automaton that gives a complete description of all infinite binary overlap-free words. Our proof is significantly simpler than those in the literature. As an application we give a complete characterization of the overlap-free words that are 2-automatic.