Relative randomness for Martin-Löf random sets

NingNing Peng, Kojiro Higuchi, Takeshi Yamazaki, Kazuyuki Tanaka

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

1 Citation (Scopus)

Abstract

Let Γ be a set of functions on the natural numbers. We introduce a new randomness notion called semi Γ-randomness, which is associated with a Γ-indexed test. Fix a computable sequence {G n} nεω of all c.e. open sets. For any f ε Γ, {G f(n)} nεω is called a Γ-indexed test if μ(G f(n)) ≤ 2 -n for all n. We prove that weak n-randomness is strictly stronger than semi Δ n 0-randomness, for n > 2. Moreover, we investigate the relationships between various definitions of randomness.

Original languageEnglish
Title of host publicationHow the World Computes - Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Proceedings
Pages581-588
Number of pages8
DOIs
Publication statusPublished - 2012 Jun 18
EventTuring Centenary Conference and 8th Conference on Computability in Europe, CiE 2012 - Cambridge, United Kingdom
Duration: 2012 Jun 182012 Jun 23

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7318 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherTuring Centenary Conference and 8th Conference on Computability in Europe, CiE 2012
CountryUnited Kingdom
CityCambridge
Period12/6/1812/6/23

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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    Peng, N., Higuchi, K., Yamazaki, T., & Tanaka, K. (2012). Relative randomness for Martin-Löf random sets. In How the World Computes - Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Proceedings (pp. 581-588). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7318 LNCS). https://doi.org/10.1007/978-3-642-30870-3_58