Combinatorial interpretation of Kolmogorov complexity
نویسندگان
چکیده
منابع مشابه
Combinatorial Interpretation of Kolmogorov Complexity
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 c...
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The Kolmogorov complexity function K can be relativized using any oracle A, and most properties of K remain true for relativized versions KA. In section 1 we provide an explanation for this observation by giving a game-theoretic interpretation and showing that all “natural” properties are either true for all KA or false for all KA if we restrict ourselves to sufficiently powerful oracles A. Thi...
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Kolmogorov complexity has intellectual roots in the areas of information theory, computability theory and probability theory. Despites its remarkably simple basis, it has some striking applications in Complexity Theory. The subject was developed by the Russian mathematician Andrei N. Kolmogorov (1903–1987) as an approach to the notion of random sequences and to provide an algorithmic approach t...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2002
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(01)00034-2