The quasi-equivalence between the definitions of partial randomness

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the recent literature, many definitions of partial randomness of reals have been proposed and studied rather discretely. For instance, it is known that for a computable real ε ∈(0, 1), strong Martin-Löf ε-randomness is strictly stronger than Solovay ε-randomness which is strictly stronger than weak Martin-Löf ε-randomness. In the present work, we firstly give several new definitions of partial randomness - strong Kolmogorov ε-randomness and weak/strong DH-Chaitin ε-randomness. Then, we investigate the relation between ε-randomness by one definition and ε′-randomness by another. Finally, we show that all of the known definitions of ε-randomness are quasi-equivalent.

Original languageEnglish
Title of host publicationProceedings - 4th International Conference on Natural Computation, ICNC 2008
Pages371-375
Number of pages5
DOIs
Publication statusPublished - 2008 Dec 22
Event4th International Conference on Natural Computation, ICNC 2008 - Jinan, China
Duration: 2008 Oct 182008 Oct 20

Publication series

NameProceedings - 4th International Conference on Natural Computation, ICNC 2008
Volume1

Other

Other4th International Conference on Natural Computation, ICNC 2008
CountryChina
CityJinan
Period08/10/1808/10/20

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Computational Mechanics

Cite this

Liu, C. G., Tanaka, K., & Yamazaki, T. (2008). The quasi-equivalence between the definitions of partial randomness. In Proceedings - 4th International Conference on Natural Computation, ICNC 2008 (pp. 371-375). [4666871] (Proceedings - 4th International Conference on Natural Computation, ICNC 2008; Vol. 1). https://doi.org/10.1109/ICNC.2008.916