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Kolmogorov Complexity in perspective. Part I: Information Theory and Randomnes (1010.3201v1)
Published 15 Oct 2010 in cs.LO, cs.CC, cs.IT, and math.IT
Abstract: 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.