Kolmogorov Complexity and Solovay Functions

Authors Laurent Bienvenu, Rod Downey



PDF
Thumbnail PDF

File

LIPIcs.STACS.2009.1810.pdf
  • Filesize: 182 kB
  • 12 pages

Document Identifiers

Author Details

Laurent Bienvenu
Rod Downey

Cite As Get BibTex

Laurent Bienvenu and Rod Downey. Kolmogorov Complexity and Solovay Functions. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 147-158, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009) https://doi.org/10.4230/LIPIcs.STACS.2009.1810

Abstract

Solovay (1975) proved that there exists a computable upper bound~$f$ of the prefix-free Kolmogorov complexity function~$K$ such that $f(x)=K(x)$ for infinitely many~$x$. In this paper, we consider the class of computable functions~$f$ such that $K(x) \leq f(x)+O(1)$ for all~$x$ and $f(x) \leq K(x)+O(1)$ for infinitely many~$x$, which we call Solovay functions. We show that Solovay functions present interesting connections with randomness notions such as Martin-L\"of randomness and K-triviality.

Subject Classification

Keywords
  • Algorithmic randomness
  • Kolmogorov complexity
  • K-triviality

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail