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

Marie Ferbus-Zanda (1) , Serge Grigorieff (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

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-Löf, Schnorr, Chaitin, Levin, and has gained new impetus in the last years.

Mots clés: Logic; Computer Science; Algoritmmic Information Theory; Shannon Information Theory; Kolmogorov Complexity; Randomness.; Randomness

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]; Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Marie Ferbus-Zanda, Serge Grigorieff. Kolmogorov Complexity in perspective. Part I: Information Theory and Randomnes. Synthese, 2010, pp.00. ⟨hal-00525504⟩