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

Published online by Cambridge University Press:  17 July 2014

Robert Mercaş
Christian-Albrechts-Universität zu Kiel, Institut für Informatik, Germany..
Pascal Ochem
CNRS, LIRMM, France.;
Alexey V. Samsonov
Ural Federal University, Ekaterinburg, Russia.; ; ;
Arseny M. Shur
Ural Federal University, Ekaterinburg, Russia.; ; ;
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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.

Research Article
© EDP Sciences 2014

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