Titlebook: Kolmogorov Complexity and Computational Complexity; Osamu Watanabe Book 1992 Springer-Verlag Berlin Heidelberg 1992 Kolmogorov.Kolmogorov

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Introduction,type of question, namely, that of Kolmogorov complexity theory. The theory was established through independent works by R.J. Solmonoff [Sol64], A.N. Kolmogorov [Kol65], and G.J. Chaitin [Cha69], and it has been shown to be an important subject in both mathematics and computer science. In particular,

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Applications of Time-Bounded Kolmogorov Complexity in Complexity Theory,ns of this approach to different questions in complexity theory. Connections will be drawn among the following topics: NE predicates, ranking functions, pseudorandom generators, and hierarchy theorems in circuit complexity.

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Kolmogorov Complexity, Complexity Cores, and the Distribution of Hardness,every problem decidable in exponential space is efficiently reducible to every complete problem, so each complete problem must have a highly organized structure. The authors have recently exploited this fact to prove that complete problems are, in two respects, . for problems in expontential space.

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Complexity and Entropy: An Introduction to the Theory of Kolmogorov Complexity,ple or complex, and their complexity can also be measured by a number. I do not know to whom we are indebted for measuring sizes by numbers. It was Andrei Kolmogorov [Kol65] who proposed to measure the complexity of a thing by a natural number (i.e., a non-negative integer), and he developed the rud

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978-3-642-77737-0Springer-Verlag Berlin Heidelberg 1992

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Kolmogorov Complexity and Computational Complexity978-3-642-77735-6Series ISSN 1431-2654 Series E-ISSN 2193-2069