A series of experiments to validate the Coding theorem method to evaluate Kolmogorov complexity based on approximations to Levin's Universal Distribution are presented, showing that the measure is stable in the face of changes in computational formalism and that results are in agreement with the results obtained using lossless compression algorithms. We found that strings which are more random according to the Coding theorem method also turn out to be less compressible, while less random strings are clearly more compressible. We also introduce a Block Matrix Decomposition technique with an application to classification of space-time evolutions of cellular automata, providing further evidence of the soundness and readiness of the Coding theorem method as an alternative and complementation to compression algorithms for approximating Kolmogorov complexity, specially for small objects (e.g. short strings and small images) where lossless compression algorithms fail.
Two-Dimensional Kolmogorov Complexity and Validation of the Coding Theorem Method by Compressibility
Hector Zenil, Fernando Soler-Toscano, Jean-Paul Delahaye, Nicolas Gauvrit