Abstract

Algorithmic information theory has a wide range of applications, despite the fact that its core quantity, Kolmogorov complexity, is incomputable. Most importantly, AIT allows to quantify Occam’s razor, the core scientific paradigm that ”among two models that describe the data equally well, the simpler one should be preferred”. This led to universal theories of induction and action in the field of machine learning and artificial intelligence, and practical versions like the Minimum Encoding Length (MDL/MML) principles. The universal similarity metric probably spawned the greatest practical success of AIT . Approximated by standard compressors like Lempel-Ziv (zip) or bzip2 or PPMZ , it leads to the normalized compression distance, which has been used to fully automatically reconstruct language and phylogenetic trees, and many other clustering problems. AIT has been applied in disciplines as remote as Cognitive Sciences, Biology, Physics, and Economics.