Algorithmic information theory

Peter D. Grunwald; Paul M. B. Vitanyi

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arXiv · 0809.2754

Algorithmic information theory

Peter D. Grunwald·Paul M. B. Vitanyi

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Abstract

We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are fundamentally different. We indicate how recent developments within the theory allow one to formally distinguish between `structural' (meaningful) and `random' information as measured by the Kolmogorov structure function, which leads to a mathematical formalization of Occam's razor in inductive inference. We end by discussing some of the philosophical implications of the theory.

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BibTeX RIS

Peter D. Grunwald, Paul M. B. Vitanyi. 2008-09-17. Algorithmic information theory. https://arxiv.org/abs/0809.2754

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