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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
Support vector machine learning algorithm and transduction
TL;DR: A recently developed method to transform the original input vectors into high-dimensional space, and then construct a linear regression function or hyperplane in that space by applying the kernel technique is reviewed.
Proceedings ArticleDOI
N-gram IDF: A Global Term Weighting Scheme Based on Information Distance
TL;DR: N-gram IDF is proposed, a theoretical extension of IDF that enables to determine dominant N-grams among overlapping ones and extract key terms of any length from texts without using any NLP techniques, and was competitive with state-of-the-art methods that were designed for each application using additional resources and efforts.
Book ChapterDOI
Segmentation and morphology
TL;DR: 11 Introduction 41.1 Generalremarks 41.2 Morphology 61.3 Staticanddynamicmetaphors 92 Unsupervisedlearning ofwords 112.1 Thetwoproblemsofwordsegmentation 112.2 Trawling forchunks 142.3 Word Boundary detectors 212.4 Successesandfailures inwordse segmentation 223 Unsuper supervisedlearning ofmorphology 233.
Posted Content
On the Kolmogorov-Chaitin Complexity for short sequences
Jean-Paul Delahaye,Hector Zenil +1 more
TL;DR: An empirical approach is suggested to overcome the difficulty and obtain a stable definition of the Kolmogorov-Chaitin complexity for short sequences and a correlation in terms of distribution frequencies was found across the output of two models of abstract machines, namely unidimensional cellular automata and deterministic Turing machine.
Journal ArticleDOI
Predictive Rate-Distortion for Infinite-Order Markov Processes
TL;DR: This work casts predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics, and shows that the resulting algorithms yield substantial improvements.
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.