Complexity oscillations in random reals

Chen Guang Liu, Kazuyuki Tanaka

Research output: Contribution to journalArticlepeer-review


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
Issue number10
Publication statusPublished - 2008 Oct
Externally publishedYes


  • 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


Dive into the research topics of 'Complexity oscillations in random reals'. Together they form a unique fingerprint.

Cite this