On the growth rates of complexity of threshold languages

Arseny M. Shur; Irina A. Gorbunova

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 44, Issue: 1, page 175-192
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Shur, Arseny M., and Gorbunova, Irina A.. "On the growth rates of complexity of threshold languages." RAIRO - Theoretical Informatics and Applications 44.1 (2010): 175-192. <http://eudml.org/doc/250770>.

@article{Shur2010,
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.},
author = {Shur, Arseny M., Gorbunova, Irina A.},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Power-free languages; Dejean's conjecture; threshold languages; combinatorial complexity; growth rate.; power-free languages; growth rate},
language = {eng},
month = {2},
number = {1},
pages = {175-192},
publisher = {EDP Sciences},
title = {On the growth rates of complexity of threshold languages},
url = {http://eudml.org/doc/250770},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Shur, Arseny M.
AU - Gorbunova, Irina A.
TI - On the growth rates of complexity of threshold languages
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/2//
PB - EDP Sciences
VL - 44
IS - 1
SP - 175
EP - 192
AB - 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.
LA - eng
KW - Power-free languages; Dejean's conjecture; threshold languages; combinatorial complexity; growth rate.; power-free languages; growth rate
UR - http://eudml.org/doc/250770
ER -

References

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