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.
Mots clés : formal languages, avoidability, avoidable pattern, cube-free word, overlap-free word, growth rate, morphism
@article{ITA_2014__48_4_369_0,
author = {Merca\c{s}, Robert and Ochem, Pascal and Samsonov, Alexey V. and Shur, Arseny M.},
title = {Binary patterns in binary cube-free words: {Avoidability} and growth},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {369--389},
publisher = {EDP-Sciences},
volume = {48},
number = {4},
year = {2014},
doi = {10.1051/ita/2014015},
mrnumber = {3302493},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2014015/}
}
TY - JOUR AU - Mercaş, Robert AU - Ochem, Pascal AU - Samsonov, Alexey V. AU - Shur, Arseny M. TI - Binary patterns in binary cube-free words: Avoidability and growth JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2014 SP - 369 EP - 389 VL - 48 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2014015/ DO - 10.1051/ita/2014015 LA - en ID - ITA_2014__48_4_369_0 ER -
%0 Journal Article %A Mercaş, Robert %A Ochem, Pascal %A Samsonov, Alexey V. %A Shur, Arseny M. %T Binary patterns in binary cube-free words: Avoidability and growth %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2014 %P 369-389 %V 48 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2014015/ %R 10.1051/ita/2014015 %G en %F ITA_2014__48_4_369_0
Mercaş, Robert; Ochem, Pascal; Samsonov, Alexey V.; Shur, Arseny M. Binary patterns in binary cube-free words: Avoidability and growth. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 4, pp. 369-389. doi : 10.1051/ita/2014015. http://www.numdam.org/articles/10.1051/ita/2014015/
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