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 α ≈ 1.242 as k tends to infinity.
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