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arXiv · 1301.4682

Binary Patterns in Binary Cube-Free Words: Avoidability and Growth

Robert Mercas·Pascal Ochem·Alexei V. Samsonov·Arseny M. Shur
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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.

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Robert Mercas, Pascal Ochem, Alexei V. Samsonov, Arseny M. Shur. 2013-01-20. Binary Patterns in Binary Cube-Free Words: Avoidability and Growth. https://doi.org/10.1051/ita/2014015

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