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On the growth rates of complexity of threshold languages

Published online by Cambridge University Press:  11 February 2010

Arseny M. Shur  and
Irina A. Gorbunova
Arseny M. Shur
Affiliation:
Ural State University, Ekaterinburg, Russia; Arseny.Shur@usu.ru
Irina A. Gorbunova
Affiliation:
Ural State University, Ekaterinburg, Russia; Arseny.Shur@usu.ru
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Abstract

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 $\hat{\alpha}\approx1.242$ as k tends to infinity.

Keywords

Power-free languagesDejean's conjecturethreshold languagescombinatorial complexitygrowth rate.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 1: Special issue dedicated to the 12th "Journées Montoises d'Informatique Théorique" , January 2010 , pp. 175 - 192
Copyright
© EDP Sciences, 2010

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