MERCAS, R. ... et al, 2014. Binary patterns in binary cube-free words: avoidability and growth. RAIRO - Theoretical Informatics and Applications, 48 (4), pp.369-389
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.
The original publication is available at www.rairo-ita.org.