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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 ,
Pascal Ochem ,
Alexey V. Samsonov  and
Arseny M. Shur
Robert Mercaş
Affiliation:
Christian-Albrechts-Universität zu Kiel, Institut für Informatik, Germany.. rgm@informatik.uni-kiel.de
Pascal Ochem
Affiliation:
CNRS, LIRMM, France.; Pascal.Ochem@lirmm.fr
Alexey V. Samsonov
Affiliation:
Ural Federal University, Ekaterinburg, Russia.; vonosmas@gmail.com ; Arseny.Shur@usu.ru ;
Arseny M. Shur
Affiliation:
Ural Federal University, Ekaterinburg, Russia.; vonosmas@gmail.com ; Arseny.Shur@usu.ru ;

Abstract

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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.

Keywords

Formal languagesavoidabilityavoidable patterncube-free wordoverlap-free wordgrowth ratemorphism

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