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Binary patterns in binary cube-free words: Avoidability and growth

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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Submitted on : Thursday, January 28, 2016 - 12:22:35 PM
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Robert Mercaş, Pascal Ochem, Alexey V. Samsonov, Arseny M. Shur. Binary patterns in binary cube-free words: Avoidability and growth. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2014, 48 (4), pp.369-389. ⟨10.1051/ita/2014015⟩. ⟨lirmm-01263848⟩



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