Space-Bounded Kolmogorov Extractors

TL;DR

This paper explores space-bounded Kolmogorov extractors, demonstrating their existence using derandomization techniques and pseudo-random generators to improve randomness extraction within computational resource limits.

Contribution

It introduces a resource-bounded version of Kolmogorov extractors and proves their existence using derandomization with Nisan-Wigderson generators.

Findings

Existence of space-bounded Kolmogorov extractors proven.

Application of Nisan-Wigderson generator for derandomization.

Extension of Kolmogorov extractor theory to resource-bounded settings.

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.