Geodesic
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

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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.

DOI : 10.1051/ita/2014015
Classification : 68Q70, 68R15
Keywords: 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://geodesic.mathdoc.fr/articles/10.1051/ita/2014015/}
}
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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

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