Space-Bounded Kolmogorov Extractors

Abstract

An extractor is a function that receives some randomness and either "improves" it or produces "new" randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov extractors and modify it to resource-bounded version of Kolmogorov complexity. Following Zimand we prove the existence of such objects with certain parameters. The utilized technique is "naive" derandomization: we replace random constructions employed by Zimand by pseudo-random ones obtained by Nisan-Wigderson generator.

arXiv comment12 pages, accepted to CSR2012

References in corpus (3)

• Possibilities and impossibilities in Kolmogorov complexity extraction
• Extracting the Kolmogorov Complexity of Strings and Sequences from Sources with Limited Independence
• Symmetry of information and bounds on nonuniform randomness extraction via Kolmogorov extractors