On possible growths of arithmetical complexity

Anna E. Frid

RAIRO - Theoretical Informatics and Applications (2006)

  • Volume: 40, Issue: 3, page 443-458
  • ISSN: 0988-3754

Abstract

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The arithmetical complexity of infinite words, defined by Avgustinovich, Fon-Der-Flaass and the author in 2000, is the number of words of length n which occur in the arithmetical subsequences of the infinite word. This is one of the modifications of the classical function of subword complexity, which is equal to the number of factors of the infinite word of length n. In this paper, we show that the orders of growth of the arithmetical complexity can behave as many sub-polynomial functions. More precisely, for each sequence u of subword complexity ƒu(n) and for each prime p ≥ 3 we build a Toeplitz word on the same alphabet whose arithmetical complexity is a ( n ) = Θ ( n f u ( ⌈ log p n ⌉ ) ) .

How to cite

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Frid, Anna E.. "On possible growths of arithmetical complexity." RAIRO - Theoretical Informatics and Applications 40.3 (2006): 443-458. <http://eudml.org/doc/249690>.

@article{Frid2006,
abstract = { The arithmetical complexity of infinite words, defined by Avgustinovich, Fon-Der-Flaass and the author in 2000, is the number of words of length n which occur in the arithmetical subsequences of the infinite word. This is one of the modifications of the classical function of subword complexity, which is equal to the number of factors of the infinite word of length n. In this paper, we show that the orders of growth of the arithmetical complexity can behave as many sub-polynomial functions. More precisely, for each sequence u of subword complexity ƒu(n) and for each prime p ≥ 3 we build a Toeplitz word on the same alphabet whose arithmetical complexity is $a(n)=\Theta(n f_u(\lceil \log_p n \rceil))$. },
author = {Frid, Anna E.},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Arithmetical complexity; infinite word; subword complexity; Toeplitz word; bispecial words.; arithmetical complexity; bispecial words},
language = {eng},
month = {10},
number = {3},
pages = {443-458},
publisher = {EDP Sciences},
title = {On possible growths of arithmetical complexity},
url = {http://eudml.org/doc/249690},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Frid, Anna E.
TI - On possible growths of arithmetical complexity
JO - RAIRO - Theoretical Informatics and Applications
DA - 2006/10//
PB - EDP Sciences
VL - 40
IS - 3
SP - 443
EP - 458
AB - The arithmetical complexity of infinite words, defined by Avgustinovich, Fon-Der-Flaass and the author in 2000, is the number of words of length n which occur in the arithmetical subsequences of the infinite word. This is one of the modifications of the classical function of subword complexity, which is equal to the number of factors of the infinite word of length n. In this paper, we show that the orders of growth of the arithmetical complexity can behave as many sub-polynomial functions. More precisely, for each sequence u of subword complexity ƒu(n) and for each prime p ≥ 3 we build a Toeplitz word on the same alphabet whose arithmetical complexity is $a(n)=\Theta(n f_u(\lceil \log_p n \rceil))$.
LA - eng
KW - Arithmetical complexity; infinite word; subword complexity; Toeplitz word; bispecial words.; arithmetical complexity; bispecial words
UR - http://eudml.org/doc/249690
ER -

References

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