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

Robert Mercaş; Pascal Ochem; Alexey V. Samsonov; Arseny M. Shur

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2014)

- Volume: 48, Issue: 4, page 369-389
- ISSN: 0988-3754

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topMercaş, Robert, et al. "Binary patterns in binary cube-free words: Avoidability and growth." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 48.4 (2014): 369-389. <http://eudml.org/doc/273030>.

@article{Mercaş2014,

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.},

author = {Mercaş, Robert, Ochem, Pascal, Samsonov, Alexey V., Shur, Arseny M.},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {formal languages; avoidability; avoidable pattern; cube-free word; overlap-free word; growth rate; morphism},

language = {eng},

number = {4},

pages = {369-389},

publisher = {EDP-Sciences},

title = {Binary patterns in binary cube-free words: Avoidability and growth},

url = {http://eudml.org/doc/273030},

volume = {48},

year = {2014},

}

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

PB - EDP-Sciences

VL - 48

IS - 4

SP - 369

EP - 389

AB - 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.

LA - eng

KW - formal languages; avoidability; avoidable pattern; cube-free word; overlap-free word; growth rate; morphism

UR - http://eudml.org/doc/273030

ER -

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