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An Introduction to Kolmogorov Complexity and Its Applications
Ming Li,Paul M. B. Vitányi +1 more
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TLDR
The book presents a thorough treatment of the central ideas and their applications of Kolmogorov complexity with a wide range of illustrative applications, and will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics.Abstract:
The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field. Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and their applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, KolmogorovLoveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.read more
Citations
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Journal ArticleDOI
Sequential codes, lossless compression of individual sequences, and Kolmogorov complexity
John C. Kieffer,En-hui Yang +1 more
TL;DR: It is shown that any sequential code in the class compresses some individual sequence at a rate strictly greater than the rate for that sequence given by the OPTA function.
Journal ArticleDOI
Lower Bounds on Mutual Information
TL;DR: It is shown that non-trivial lower bounds on MI in terms of linear correlations depend on the marginal (single variable) distributions, and with gene expression data that these bounds are in general nontrivial.
Journal ArticleDOI
Complexity of Social Systems
TL;DR: In this paper, a survey of characteristics of complex systems and typology of various kinds of complexity, and of their sources is presented, and it is also shown that broadly defined human systems (human systems) are aected by all kinds of complexities.
Proceedings ArticleDOI
The quantum adversary method and classical formula size lower bounds
TL;DR: Two new complexity measures for Boolean functions are introduced, one of which, sumPI, is always at least as large as sumPI(f), and is derived from sumPI in such a way that maxPI/sup 2/(f) remains a lower bound on formula size.
Journal ArticleDOI
Roughian: Rough information analysis
Ivo Düntsch,Günther Gediga +1 more
TL;DR: A sequence of papers and conference contributions have developed the components of a non‐invasive method of data analysis, which is based on the RSDA principle, but is not restricted to “classical” RSDA applications.
References
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Journal ArticleDOI
On Computable Numbers, with an Application to the Entscheidungsproblem
TL;DR: This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.
Journal ArticleDOI
Simulating physics with computers
TL;DR: In this paper, the authors describe the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations, and the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature.
Proceedings ArticleDOI
The complexity of theorem-proving procedures
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
Book ChapterDOI
On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
TL;DR: This chapter reproduces the English translation by B. Seckler of the paper by Vapnik and Chervonenkis in which they gave proofs for the innovative results they had obtained in a draft form in July 1966 and announced in 1968 in their note in Soviet Mathematics Doklady.
Journal ArticleDOI
A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.