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

dmtcs:2696 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2696
Bounds of asymptotic occurrence rates of some patterns in binary words related to integer-valued logistic mapsArticle

Authors: Koji Nuida 1

  • 1 Research Center for Information Security

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.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: binary word,pattern occurrence rate,simple normality,logistic map,pseudorandom number generator,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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