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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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Proceedings ArticleDOI
Thermodynamics of computation and information distance
TL;DR: In this article, the authors compare several candidates for an asymptotically machine-independent algorithm for reversible computation and show that the maximum of the conditional Kolmogorov complexities is optimal, in the sense of being minimal within an additive constant among semicomputable, symmetric, positive semidefinite functions of z and y satisfying a reasonable normalization condition.
Book ChapterDOI
Emergence in Agent based Computational Social Science: conceptual, formal and diagrammatic analysis.
TL;DR: In this paper, a critical survey of emergence definitions both from a conceptual and formal standpoint is provided, with particular attention devoted to formal definitions introduced by (Muller 2004) and (Bonabeau & Dessalles, 1997), which are operative in multi-agent frameworks and make sense from both cognitive and social point of view.
A computational model of the emergence of early constructions
TL;DR: This thesis explores and formalizes the view that grammar learning is driven by meaningful language use in context, and presents a computational model in which all aspects of the language learning problem are reformulated in line with these assumptions.
Journal ArticleDOI
The complexity of gene expression dynamics revealed by permutation entropy
Xiaoliang Sun,Xiaoliang Sun,Yong Zou,Victoria J. Nikiforova,Jürgen Kurths,Jürgen Kurths,Jürgen Kurths,Dirk Walther +7 more
TL;DR: It is shown that Permutation Entropy is a simple yet robust and powerful approach to identify temporal gene expression profiles of varying complexity that is equally applicable to other types of molecular profile data.
Journal ArticleDOI
Asymptotic Behaviour and Ratios of Complexity in Cellular Automata
TL;DR: Using two different measures, Shannon's block entropy and Kolmogorov complexity, the latter approximated by two different methods (lossless compressibility and block decomposition), the trend of larger complex behavioural fractions is arrived at.
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.