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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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An algebra of human concept learning
TL;DR: This paper investigates the structure of patterns in data defined over discrete features, i.e. features with two or more qualitatively distinct values, by extending the basic theory of algebraic decomposition to include algebraic accounts of the typicality of individual objects within concepts, and estimation of the power series from noisy data.
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Exploiting compositionality to explore a large space of model structures
TL;DR: This work organizes a space of matrix decomposition models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules and automatically chooses the decomposition structure from raw data by evaluating only a small fraction of all models.
Posted Content
Energy-Efficient Algorithms
TL;DR: This work proposes energy-aware variations of three standard models of computation: circuit RAM, word RAM, and transdichotomous RAM that build familiar high-level primitives such as control logic, memory allocation, and garbage collection with zero energy complexity and only constant-factor overheads in space and time complexity.
Supplementary Material for Textual Data Compression in Computational Biology: A synopsis
TL;DR: In this paper, the main strategy of algorithms in this class is to substitute repeated strings, i.e., exact replicas of a substring in a string, within the text with a convenient coding scheme.
Journal ArticleDOI
On the optimization of classes for the assignment of unidentified reading frames in functional genomics programmes: the need for machine learning
Douglas B. Kell,Ross D. King +1 more
TL;DR: The present functional classes are suboptimal and new unsupervised clustering methods are needed to improve them, and better-structured functional classes will facilitate the prediction of biochemically testable functions.
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.