kolmogorov-compression

Kolmogorov complexity measures compressibility by finding the shortest program that outputs target data. This Skill approximates K(x) by generating minimal Python programs via LLM-based code generation, then calculates program length and an intelligence score to quantify compression efficiency across strings and datasets.

Kolmogorov complexity represents the theoretical shortest program needed to produce a given string, providing a mathematical foundation for understanding data structure and randomness. It connects to universal induction and Turing machines, enabling compression-based intelligence evaluation where simpler data compresses more than complex or random data.

Compression-based evaluation applies Kolmogorov principles to assess model outputs by generating the shortest program reproducing that output and computing its length. Lower compression indicates simpler, more structured responses; higher compression suggests random or complex outputs, enabling quantitative intelligence scoring across model generations.

Yes. This Skill uses approximate methods inspired by KoLMogorov-Test, leveraging LLMs and code generators to find near-minimal programs instead of provably shortest ones. The approximation produces practical intelligence scores and compression metrics suitable for real-world datasets while acknowledging Kolmogorov complexity's theoretical uncomputability.

The Skill accepts strings, datasets, and model outputs as input, generating Python programs that reproduce the exact input. It computes program length across these formats using conditional complexity principles, enabling compression efficiency scoring for diverse data structures without format conversion.

Approximations depend on the LLM's ability to generate genuinely minimal programs and may not reach theoretical shortest length. Program length estimates reflect code generator capability rather than true K(x), and very large datasets may exceed practical generation constraints, requiring awareness that results estimate rather than prove complexity bounds.