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.
|出版ステータス||出版済み - 2009|
|イベント||21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, オーストリア|
継続期間: 7 20 2009 → 7 24 2009
|その他||21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09|
|Period||7/20/09 → 7/24/09|
All Science Journal Classification (ASJC) codes