Complexity oscillations in random reals

Chen Guang Liu, Kazuyuki Tanaka

Research output: Contribution to journalArticlepeer-review

Abstract

The C-oscillation due to Martin-Löf shows that {a\ Vn[C(α → n) ≥ n - O(1)]} = θ, which also follows {α\in[K(α \ n) ≥ n + K(n) - O(1)]} = θ. By generalizing them, we show that there does not exist a real α such that Vn (K(α \ n)≥n + λK(n) - O(1)) for any λ > 0.

Original languageEnglish
Pages (from-to)2517-2518
Number of pages2
JournalIEICE Transactions on Information and Systems
VolumeE91-D
Issue number10
DOIs
Publication statusPublished - 2008 Oct

Keywords

  • Algorithmic randomness
  • C-oscillation
  • Kolmogorov complexity

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering
  • Artificial Intelligence

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