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Discrete Mathematics & Theoretical Computer Science |
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.
Source : ScholeXplorer
IsRelatedTo DOI 10.1103/physreve.51.3670 Source : ScholeXplorer IsRelatedTo PMID 9963048
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