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

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

In: Mathematics, Vol. 7, No. 9, 838, 01.09.2019.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ef030fe24440486cb79e34bbda9682ff,

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

abstract = "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.",

keywords = "K- distributed numbers, Normal numbers, Pseudorandom number generator, Random number generator, Randomness, Shannon entropy, Stochastic process, Two-faced processes, normal numbers, stochastic process, two-faced processes, randomness, random number generator, pseudorandom number generator, k-distributed numbers",

author = "Boris Ryabko",

note = "Publisher Copyright: {\textcopyright} 2019 by the authors.",

year = "2019",

month = sep,

day = "1",

doi = "10.3390/math7090838",

language = "English",

volume = "7",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "9",

}

RIS

TY - JOUR

T1 - Low-entropy stochastic processes for generating k-distributed and normal sequences, and the relationship of these processes with random number generators

AU - Ryabko, Boris

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - K- distributed numbers

KW - Normal numbers

KW - Pseudorandom number generator

KW - Random number generator

KW - Randomness

KW - Shannon entropy

KW - Stochastic process

KW - Two-faced processes

KW - normal numbers

KW - stochastic process

KW - two-faced processes

KW - randomness

KW - random number generator

KW - pseudorandom number generator

KW - k-distributed numbers

UR - http://www.scopus.com/inward/record.url?scp=85072340331&partnerID=8YFLogxK

U2 - 10.3390/math7090838

DO - 10.3390/math7090838

M3 - Article

AN - SCOPUS:85072340331

VL - 7

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 9

M1 - 838

ER -

ID: 21609479