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Mathematics - Computational Science & Engineering | Selected Works of A. N. Kolmogorov - Volume III: Information Theory and the Theory of Algorithms

Selected Works of A. N. Kolmogorov

Volume III: Information Theory and the Theory of Algorithms

Shiryayev, A.N. (Ed.)

Originally published in Russian

1993, XXV, 275 p.

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Content Level » Research

Keywords » Calculation - Information - Invariant - Morphism - algorithmic information theory - algorithms - calculus - complexity - entropy - function - information theory

Related subjects » Computational Science & Engineering - Security and Cryptology - Theoretical Computer Science

Table of contents 

Papers by A. V. Kolmogorov.- 1. On the notion of algorithm.- 2. On the general definition of the quantity of information.- 3. The theory of transmission of information.- 4. Amount of information and entropy for continuous distributions.- 5. New metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces.- 6. To the definition of algorithms.- 7. ?-entropy and ?-capacity of sets in functional spaces.- 8. Various approaches to estimating the complexity of approximate representation and calculation of functions.- 9. On tables of random numbers.- 10. Three approaches to the definition of the notion of amount of information.- 11. On the realization of networks in three — dimensional space.- 12. To the logical foundations of the theory of information and probability theory.- 13. The combinatorial foundations of information theory and the probability calculus.- Comments and addenda.- On works in information theory and some of its applications.- Information theory.- Algorithmic information theory.- ?-entropy and ?-capacity.- Tables of random numbers.- Realization of networks in 3-dimensional space.- Ergodic theory.- Kolmogorov’s algorithms or machines.- From A. N. Kolmogorov’s recollections.- Appendix 1. Report to the mathematical circle about square pavings.- Appendix 2. On operations on sets. II.- Afterword.

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