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### 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},