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Kolmogorov Complexity as a Language

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Computer Science – Theory and Applications (CSR 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6651))

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Abstract

The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal comments) many different examples where notions and statements that involve Kolmogorov complexity are compared with their counterparts not involving complexity.

Supported in part by NAFIT ANR-08-EMER-008-01 grant. Author is grateful to all the participants of Kolmogorov seminar at Moscow State University and to his LIF/ESCAPE colleagues. Many of the results covered in this survey were obtained (or at least inspired) by Andrej Muchnik (1958–2007).

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Author information

Authors and Affiliations

  1. LIF Marseille, CNRS & Univ. Aix–Marseille, France

    Alexander Shen

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  1. Alexander Shen
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Editor information

Editors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, 191023, St.Petersburg, Russia

    Alexander Kulikov

  2. Department of Mathematical Logic and Theory of Algorithms, Moscow State University, Leninskie gory, 119991, Moscow, Russia

    Nikolay Vereshchagin

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Shen, A. (2011). Kolmogorov Complexity as a Language. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_9

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  • DOI: https://doi.org/10.1007/978-3-642-20712-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20711-2

  • Online ISBN: 978-3-642-20712-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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