English

Fife's Theorem Revisited

Formal Languages and Automata Theory 2011-07-28 v3

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.

Keywords

Cite

@article{arxiv.1102.3932,
  title  = {Fife's Theorem Revisited},
  author = {Jeffrey Shallit},
  journal= {arXiv preprint arXiv:1102.3932},
  year   = {2011}
}
R2 v1 2026-06-21T17:28:40.196Z