On the growth rates of complexity of threshold languages
Shur, Arseny M. ; Gorbunova, Irina A.
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010), p. 175-192 / Harvested from Numdam
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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.

Publié le : 2010-01-01
DOI : https://doi.org/10.1051/ita/2010012
Classification:  68Q70,  68R15 
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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},
     volume = {44},
     year = {2010},
     pages = {175-192},
     doi = {10.1051/ita/2010012},
     mrnumber = {2604942},
     zbl = {1184.68341},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_2010__44_1_175_0}
}

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) pp. 175-192. doi : 10.1051/ita/2010012. http://gdmltest.u-ga.fr/item/ITA_2010__44_1_175_0/

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