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2 results

  • On the growth rates of complexity of threshold languages

  • Arseny M. Shur, Irina A. Gorbunova
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 44 / Issue 1 / January 2010
    Published online by Cambridge University Press:
    11 February 2010, pp. 175-192
    Print publication:
    January 2010

  • 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.