Extractors and an efficient variant of Muchnik's theorem

TL;DR

This paper introduces a new proof of Muchnik's theorem using extractors and extends it to space- and time-bounded Kolmogorov complexity, providing more efficient transformations between words.

Contribution

The paper offers a novel extractor-based proof of Muchnik's theorem and develops new versions applicable to resource-bounded Kolmogorov complexity.

Findings

New extractor-based proof of Muchnik's theorem

Extensions to space- and time-bounded Kolmogorov complexity

More efficient transformations between words under resource constraints

Abstract

Muchnik's theorem about simple conditional descriprion states that for all words $a$ and $b$ there exists a short program $p$ transforming $a$ to $b$ that has the least possible length and is simple conditional on $b$. This paper presents a new proof of this theorem, based on extractors. Employing the extractor technique, two new versions of Muchnik's theorem for space- and time-bounded Kolmogorov complexity are proven.