History of uniform random number generation

L’Ecuyer, Pierre

doi:10.1109/wsc.2017.8247790

Cited by 37 publications

(45 citation statements)

References 162 publications

(159 reference statements)

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“…It was inspired by a problem that arises in hybrid navigation systems that use both GPS and dead-reckoning sensors [40]. The third experiment, involving a step change in the parameters of a signal generator, was an analogue to a problem that may arise in evaluating multiple stream random number generators [41], where we may detect and evaluate the probability of changes in the parameters of those generators. The fourth experiment was the detection of the disappearance of noise.…”

Section: The Design Of the Experimentsmentioning

confidence: 99%

Introduction to Extreme Seeking Entropy

Vrba

Mareš

2020

Entropy

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Recently, the concept of evaluating an unusually large learning effort of an adaptive system to detect novelties in the observed data was introduced. The present paper introduces a new measure of the learning effort of an adaptive system. The proposed method also uses adaptable parameters. Instead of a multi-scale enhanced approach, the generalized Pareto distribution is employed to estimate the probability of unusual updates, as well as for detecting novelties. This measure was successfully tested in various scenarios with (i) synthetic data, (ii) real time series datasets, and multiple adaptive filters and learning algorithms. The results of these experiments are presented.

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Section: The Design Of the Experimentsmentioning

confidence: 99%

Introduction to Extreme Seeking Entropy

Vrba

Mareš

2020

Entropy

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“…The sequence is normal (or ∞-distributed) if it is k-distributed for any k ≥ 1. Borel called normal to base b a real number from the interval (0, 1) whose expansion in base b is normal sequence, and showed that almost all real numbers are normal to any base (with respect to the uniform measure) [1,2]. It is interesting that the construction of ∞-distributed sequence in an explicit form was first achieved by Champernowne in 1933 [3], who proved that the sequence 0 1 2 ...9 10 11 12 ... 99 100 101 102 ...…”

Section: Introductionmentioning

confidence: 99%

“…Later, many ∞-distributed sequences were described and investigated in numerous papers (see for review [4]). Many researchers suppose that fractional parts of π, e, and √ 2 and some other "mathematical" constants are normal, but it is not proven [2,5]. On the other hand, for π empirical counting over several billions of its digits suggests that this might be true (see [5,6]).…”

Section: Introductionmentioning

confidence: 99%

“…One of the reasons for interest in kand ∞-distributed sequences is due to the fact that they are closely related to the concept of randomness. If we imagine that someone tosses a fair coin with sides marked 0 and 1, he/she obtains (almost surely) an ∞-distributed sequence [2,5]. A mathematical model of such an experiment is a sequence of an independent and identically distributed (i.i.d.)…”

Section: Introductionmentioning

confidence: 99%

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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

2019

Mathematics

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An infinite sequence x 1 x 2 . . . 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.

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“…5, p. 84+) that such post-processing provides a new PRNG at minimal cost which is 2.5 times faster than the PRNGs which pass the whole TestU01 [16]. Moreover, it is worth noticing that most of the classical PRNGs [18,19] do not pass the TestU01.…”

Section: Introductionmentioning

confidence: 99%

Gray Codes Generation Algorithm and Theoretical Evaluation of Random Walks in N-Cubes

2018

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In previous works, some of the authors have proposed a canonical form of Gray Codes (GCs) in N-cubes (hypercubes of dimension N). This form allowed them to draw an algorithm that theoretically provides exactly all the GCs for a given dimension N. In another work, we first have shown that any of these GC can be used to build the transition function of a Pseudorandom Number Generator (PRNG). Also, we have found a theoretical quadratic upper bound of the mixing time, i.e., the number of iterations that are required to provide a PRNG whose output is uniform. This article, extends these two previous works both practically and theoretically. On the one hand, another algorithm for generating GCs is proposed that provides an efficient generation of subsets of the entire set of GCs related to a given dimension N. This offers a large choice of GC to be used in the construction of Choatic Iterations based PRNGs (CI-PRNGs), leading to a large class of possible PRNGs. On the other hand, the mixing time has been theoretically shown to be in N log(N), which was anticipated in the previous article, but not proven.

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History of uniform random number generation

Cited by 37 publications

References 162 publications

Introduction to Extreme Seeking Entropy

Introduction to Extreme Seeking Entropy

Low-Entropy Stochastic Processes for Generating k-Distributed and Normal Sequences, and the Relationship of These Processes with Random Number Generators †

Gray Codes Generation Algorithm and Theoretical Evaluation of Random Walks in N-Cubes

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