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Combinatorial interpretation of Kolmogorov complexity

By A. Romashchenko, A. Shen and N. Vereshchagin

Abstract

The very first Kolmogorov’s paper on algorithmic information theory [1] was entitled “Three approaches to the definition of the quantity of information”. These three approaches were called combinatorial, probabilistic and algorithmic. Trying to establish formal connections between combinatorial and algorithmic approaches, we prove that every linear inequality including Kolmogorov complexities could be translated into an equivalent combinatorial statement. Entropy (complexity) proofs of combinatorial inequalities given in [5] and [2] can be considered as a special cases (and a natural starting points) for this translation

Year: 2002
OAI identifier: oai:CiteSeerX.psu:10.1.1.404.7161
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