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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
What is the complexity of a distributed computing system
TL;DR: This article defines different aspects of system complexity and proposes metrics for measuring these aspects and proposes general guidelines that can help reduce the complexity of systems.
Journal ArticleDOI
Psychological complexity and the cost of information processing
TL;DR: This paper suggests that psychological complexity and processing cost can be quantified using the notion of hierarchical change and discusses the relationship between change, complexity, and the Gestalt principles of perceptual organization.
Book ChapterDOI
Efficiently Summarising Event Sequences with Rich Interleaving Patterns
TL;DR: This paper proposes SQUISH, a novel greedy MDL-based method for summarising sequential data using rich patterns that are allowed to interleave, and shows how this results in better models, as well as discovers meaningful semantics in the form patterns that identify multiple choices of values.
Journal ArticleDOI
Simulating economic transition processes by genetic programming
Shu-Heng Chen,Chia-Hsuan Yeh +1 more
TL;DR: The first application, designed for the pedagogic purpose, shows that genetic programming can simulate the non-smooth transition, which is difficult to be captured by conventional toolkits, such as differential equations and difference equations.
Journal Article
Syntax, Parsing and Production of Natural Language in a Framework of Information Compression by Multiple Alignment, Unification and Search
TL;DR: The ICMAUS framework and the SP61 model can accommodate 'context sensitive' features of syntax in a relatively simple and direct manner and can produce a sentence by decoding a compressed code for the sentence.
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.