Geodesic
On the growth rates of complexity of threshold languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 175-192

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Threshold languages, which are the (k/(k-1))+-free languages over k-letter alphabets with k ≥ 5, are the minimal infinite power-free languages according to Dejean's conjecture, which is now proved for all alphabets. We study the growth properties of these languages. On the base of obtained structural properties and computer-assisted studies we conjecture that the growth rate of complexity of the threshold language over k letters tends to a constant α ^≈1.242 as k tends to infinity.

DOI : 10.1051/ita/2010012
Classification : 68Q70, 68R15
Keywords: power-free languages, Dejean's conjecture, threshold languages, combinatorial complexity, growth rate 
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     author = {Shur, Arseny M. and Gorbunova, Irina A.},
     title = {On the growth rates of complexity of threshold languages},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {175--192},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {1},
     year = {2010},
     doi = {10.1051/ita/2010012},
     mrnumber = {2604942},
     zbl = {1184.68341},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2010012/}
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Shur, Arseny M.; Gorbunova, Irina A. On the growth rates of complexity of threshold languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 1, pp. 175-192. doi: 10.1051/ita/2010012

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