Kolmogorov Complexity in perspective. Part I: Information Theory and Randomnes

Details Kolmogorov Complexity in perspective. Part I: Information Theory and Randomnes Kolmogorov Complexity in perspective. Part I: Information Theory and Randomnes

2010-10-15

arxiv.org/abs/1010.3201v1

Synthese / Synth\`ese (2010) 00

Computer Science

Logic in Computer Science

40 pages

Scientific paper

We survey diverse approaches to the notion of information: from Shannon entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts in the same volume. Part I is dedicated to information theory and the mathematical formalization of randomness based on Kolmogorov complexity. This last application goes back to the 60's and 70's with the work of Martin-L\"of, Schnorr, Chaitin, Levin, and has gained new impetus in the last years.

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