Kolmogorov Complexity in Randomness Extraction

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

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John M. Hitchcock
Aduri Pavan
N. V. Vinodchandran

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John M. Hitchcock, Aduri Pavan, and N. V. Vinodchandran. Kolmogorov Complexity in Randomness Extraction. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 215-226, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


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 ${\cal M}_k$.
  • Extractors
  • Kolmogorov extractors
  • randomness


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