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DOI: 10.4230/LIPIcs.FSTTCS.2009.2320
URN: urn:nbn:de:0030-drops-23201
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2320/

Hitchcock, John M. ; Pavan, Aduri ; Vinodchandran, N. V.

Kolmogorov Complexity in Randomness Extraction

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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 =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2009.2320},
  annote =	{Keywords: Extractors, Kolmogorov extractors, randomness}
}

Keywords: Extractors, Kolmogorov extractors, randomness
Seminar: 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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