Bounds of asymptotic occurrence rates of some patterns in binary words related to integer-valued logistic maps

Research output: Contribution to conferencePaperpeer-review

Abstract

In this article, we investigate the asymptotic occurrence rates of specific subwords in any infinite binary word. We prove that the asymptotic occurrence rate for the subwords is upper- and lower-bounded in the same way for every infinite binary word, in terms of the asymptotic occurrence rate of the zeros. We also show that both of the bounds are best-possible by constructing, for each bound, a concrete infinite binary word such that the bound is reached. Moreover, we apply the result to analyses of recently-proposed pseudorandom number generators that are based on integer-valued variants of logistic maps.

Original languageEnglish
Pages709-720
Number of pages12
Publication statusPublished - 2009
Externally publishedYes
Event21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, Austria
Duration: Jul 20 2009Jul 24 2009

Other

Other21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09
CountryAustria
CityLinz
Period7/20/097/24/09

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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