English

On the Morse-Hedlund complexity gap

Formal Languages and Automata Theory 2012-02-02 v5 Discrete Mathematics

Abstract

In 1938, Morse and Hedlund proved that the subword complexity function of an infinite word is either bounded or at least linearly growing. In 1982, Ehrenfeucht and Rozenberg proved that this gap property holds for the subword complexity function of any language. The aim of the present paper is to present a self-contained, compact proof of Ehrenfeucht and Rozenberg's result.

Cite

@article{arxiv.0903.1627,
  title  = {On the Morse-Hedlund complexity gap},
  author = {Julien Cassaigne and Francois Nicolas},
  journal= {arXiv preprint arXiv:0903.1627},
  year   = {2012}
}

Comments

7 pages. Not intended to be submitted. New proof of an old result

R2 v1 2026-06-21T12:20:00.357Z