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On the growth rates of complexity of threshold languages

Arseny M. ShurIrina A. Gorbunova — 2010

RAIRO - Theoretical Informatics and Applications

Threshold languages, which are the (/(–1))-free languages over -letter alphabets with ≥ 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 letters tends to a constant α ^ 1 . 242 as tends to infinity.

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