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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
On initial segment complexity and degrees of randomness
Joseph S. Miller,Liang Yu +1 more
TL;DR: The main tool is another structure intended to measure the degree of randomness of real numbers: the vL-degrees, and it is shown that X ≤K Y implies X ≤vL Y, so some results can be transferred.
Journal ArticleDOI
Analyzing worms and network traffic using compression
TL;DR: This paper shows how techniques based on Kolmogorov Complexity can help in the analysis of internet worms and network traffic and shows how to use compression to detect malicious network sessions that are very similar to known intrusion attempts.
Posted Content
Natural Selection V. How to Read the Fundamental Equations of Evolutionary Change in Terms of Information Theory
TL;DR: The correct relations between statistical expressions for selection and information theory expressions for Selection are shown and those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics and communication.
Book
The Beginning and the End : The Meaning of Life in a Cosmological Perspective
TL;DR: This thesis explores foundations to build a cosmological ethics and concludes that the ultimate good is the infinite continuation of the evolutionary process.
Journal Article
Accumulative prediction error and the selection of time series models
TL;DR: The rationale for using accumulative one-step-ahead prediction error (APE) as a data-driven method for model selection is reviewed, and the possibility of using APE to discriminate the short-range ARMA(1,1) model from the long-rangeARFIMA ( 0 , d , 0 ) model is explored.
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.