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DOI: 10.4230/LIPIcs.STACS.2009.1810
URN: urn:nbn:de:0030-drops-18107
URL: http://drops.dagstuhl.de/opus/volltexte/2009/1810/
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Bienvenu, Laurent ; Downey, Rod

Kolmogorov Complexity and Solovay Functions

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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.

BibTeX - Entry

@InProceedings{bienvenu_et_al:LIPIcs:2009:1810,
  author =	{Laurent Bienvenu and Rod Downey},
  title =	{{Kolmogorov Complexity and Solovay Functions}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{147--158},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Susanne Albers and Jean-Yves Marion},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/1810},
  URN =		{urn:nbn:de:0030-drops-18107},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2009.1810},
  annote =	{Keywords: Algorithmic randomness, Kolmogorov complexity, K-triviality}
}

Keywords: Algorithmic randomness, Kolmogorov complexity, K-triviality
Seminar: 26th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2009
Date of publication: 19.02.2009


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