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

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Article number838
Number of pages10
JournalMathematics
Volume7
Issue number9
DOIs
Publication statusPublished - 1 Sep 2019

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

Fingerprint

Dive into the research topics of 'Low-entropy stochastic processes for generating k-distributed and normal sequences, and the relationship of these processes with random number generators'. Together they form a unique fingerprint.

Cite this