Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality Marie Ferbus-Zanda To cite this version: Marie Ferbus-Zanda. Kolmogorov Complexity in perspective. Part II: Classification, Information Processing and Duality. Synthese, Springer Verlag (Germany), 2010, pp.00. hal-00525505 HAL Id: hal-00525505 https://hal.archives-ouvertes.fr/hal-00525505 Submitted on 13 Oct 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Kolmogorov Complexity in perspective Part II: Classification, Information Processing and Duality∗ Marie Ferbus-Zanda LIAFA, CNRS & Universit´eParis Diderot - Paris 7 Case 7014 75205 Paris Cedex 13 France
[email protected] Abstract We survey diverse approaches to the notion of information: from Shan- non entropy to Kolmogorov complexity. Two of the main applications of Kolmogorov complexity are presented: randomness and classification. The survey is divided in two parts published in a same volume. Part II is dedicated to the relation between logic and information sys- tem, within the scope of Kolmogorov algorithmic information theory. We present a recent application of Kolmogorov complexity: classification us- ing compression, an idea with provocative implementation by authors such as Bennett, Vit´anyi and Cilibrasi.