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avoidable pattern

RAIRO - Theoretical Informatics and Applications (1)

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Binary patterns in binary cube-free words: Avoidability and growth ∗
Robert Mercaş, Pascal Ochem, Alexey V. Samsonov, Arseny M. Shur
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 48 / Issue 4 / October 2014

Published online by Cambridge University Press:

17 July 2014, pp. 369-389

Print publication:

October 2014
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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.