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

Boris Ryabko
Additional contact information
Boris Ryabko: Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Science, 630090 Novosibirsk, Russia

Mathematics, 2019, vol. 7, issue 9, 1-10

Abstract: 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.

Keywords: stochastic process; k- distributed numbers; normal numbers; random number generator; pseudorandom number generator; two-faced processes; randomness; Shannon entropy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/9/838/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/9/838/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:9:p:838-:d:265956

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().