Kolmogorov structure functions for automatic complexity

TL;DR

This paper investigates the Kolmogorov structure function in the context of nondeterministic automatic complexity, providing theoretical bounds supported by numerical evidence.

Contribution

It introduces and analyzes the Kolmogorov structure function for nondeterministic automatic complexity, establishing sharp upper bounds.

Findings

Established upper bounds on the structure function.

Provided numerical evidence supporting the bounds.

Enhanced understanding of automatic complexity measures.

Abstract

For a finite word $w$ we define and study the Kolmogorov structure function $h_w$ for nondeterministic automatic complexity. We prove upper bounds on $h_w$ that appear to be quite sharp, based on numerical evidence.