An additivity theorem for plain Kolmogorov complexity

TL;DR

This paper establishes a fundamental additivity theorem linking plain Kolmogorov complexity of pairs to conditional complexities, enhancing understanding of complexity relationships.

Contribution

It proves a new formula connecting plain and prefix complexities of pairs, clarifying their interplay in Kolmogorov complexity theory.

Findings

The formula C(a,b) = K(a|C(a,b)) + C(b|a,C(a,b)) + O(1) is established.

The result bridges plain and prefix complexity measures.

Provides a new tool for analyzing complexity of data pairs.

Abstract

We prove the formula C(a,b) = K(a|C(a,b)) + C(b|a,C(a,b)) + O(1) that expresses the plain complexity of a pair in terms of prefix and plain conditional complexities of its components.