Relative randomness for Martin-Löf random sets

Ning Ning Peng, Kojiro Higuchi, Takeshi Yamazaki, Kazuyuki Tanaka

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルHow the World Computes - Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Proceedings
ページ581-588
ページ数8
DOI
出版ステータスPublished - 2012
イベントTuring Centenary Conference and 8th Conference on Computability in Europe, CiE 2012 - Cambridge, United Kingdom
継続期間: 2012 6 182012 6 23

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7318 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

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

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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