License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2009.2320
URN: urn:nbn:de:0030-drops-23201
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/2320/
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Hitchcock, John M. ; Pavan, Aduri ; Vinodchandran, N. V.

Kolmogorov Complexity in Randomness Extraction

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09005.HitchcockJohn.2320.pdf (0.2 MB)

Abstract

We clarify the role of Kolmogorov complexity in the area of randomness
extraction. We show that a computable function is an almost
randomness extractor if and only if it is a Kolmogorov complexity
extractor, thus establishing a fundamental equivalence between two
forms of extraction studied in the literature: Kolmogorov extraction
and randomness extraction. We present a distribution ${\cal M}_k$
based on Kolmogorov complexity that is complete for randomness
extraction in the sense that a computable function is an almost
randomness extractor if and only if it extracts randomness from ${\cal
M}_k$.

BibTeX - Entry

@InProceedings{hitchcock_et_al:LIPIcs:2009:2320,
  author =	{John M. Hitchcock and Aduri Pavan and N. V. Vinodchandran},
  title =	{{Kolmogorov Complexity in Randomness Extraction}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{215--226},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-13-2},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{4},
  editor =	{Ravi Kannan and K. Narayan Kumar},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2320},
  URN =		{urn:nbn:de:0030-drops-23201},
  doi =		{10.4230/LIPIcs.FSTTCS.2009.2320},
  annote =	{Keywords: Extractors, Kolmogorov extractors, randomness}
}

Keywords: Extractors, Kolmogorov extractors, randomness
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Issue Date: 2009
Date of publication: 14.12.2009

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