Emergent Mind
Kolmogorov Complexity in perspective. Part I: Information Theory and Randomnes
(1010.3201)
Published Oct 15, 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.
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