Low-entropy stochastic processes for generating k-distributed and normal sequences, and the relationship of these processes with random number generators

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

An infinite sequence x1x2... of letters from some alphabet [0, 1, ..., b - 1], b ≥ 2, is called k-distributed (k ≥ 1) if any k-letter block of successive digits appears with the frequency b-k in the long run. The sequence is called normal (or ∞-distributed) if it is k-distributed for any k ≥ 1. We describe two classes of low-entropy processes that with probability 1 generate either k-distributed sequences or ∞-distributed sequences. Then, we show how those processes can be used for building random number generators whose outputs are either k-distributed or ∞-distributed. Thus, these generators have statistical properties that are mathematically proven.

Язык оригиналаанглийский
Номер статьи838
Число страниц10
ЖурналMathematics
Том7
Номер выпуска9
DOI
СостояниеОпубликовано - 1 сен 2019

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