An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Inequalities for Shannon entropy and Kolmogorov complexity
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
A strange application of Kolmogorov complexity
A strange application of Kolmogorov complexity
Partitioning multi-dimensional sets in a small number of "Uniform" parts
European Journal of Combinatorics
A Random Oracle Does Not Help Extract the Mutual Information
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Stability of properties of Kolmogorov complexity under relativization
Problems of Information Transmission
Kolmogorov complexity as a language
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Multisource algorithmic information theory
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
On the combinatorial representation of information
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
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Kolmogorov's very first paper on algorithmic information theory (Kolmogorov, Problemy peredachi informatsii 1(1) (1965) 3) 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. (Note that the same linear inequalities are true for Kolmogorov complexity and Shannon entropy, see Hammer et al., (Proceedings of CCC'97, Ulm).) Entropy (complexity) proofs of combinatorial inequalities given in Llewellyn and Radhakrishnan (Personal Communication) and Hammer and Shen (Theory Comput. Syst. 31 (1998) 1) can be considered as special cases (and natural starting points) for this translation.