Binary Patterns in Binary Cube-Free Words: Avoidability and Growth
Formal Languages and Automata Theory
2019-02-20 v1 Combinatorics
Abstract
The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper bounds. Finally, a new example of a pattern-avoiding language of polynomial growth is given.
Keywords
Cite
@article{arxiv.1301.4682,
title = {Binary Patterns in Binary Cube-Free Words: Avoidability and Growth},
author = {Robert Mercas and Pascal Ochem and Alexei V. Samsonov and Arseny M. Shur},
journal= {arXiv preprint arXiv:1301.4682},
year = {2019}
}
Comments
18 pages, 2 tables; submitted to RAIRO TIA (Special issue of Mons Days 2012)