Kolmogorov Complexity in Randomness Extraction

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 Mk 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 Mk.

• Type: Conference
• Year: 2009
• Where: FSTTCS
• Authors: John M. Hitchcock, Aduri Pavan, N. V. Vinodchandran
• Keywords: FSTTCS 2009, Kolmogorov Complexity, Randomness Extraction, Randomness Extractor, Theoretical Computer Science