Binary patterns in binary cube-free words: avoidability and growth
journal contributionposted on 31.03.2017, 11:59 by Robert Mercas, Pascal Ochem, Alexey V. Samsonov, Arseny M. Shur
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.
- Computer Science