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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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Book ChapterDOI
Using MDL for grammar induction
TL;DR: It is proved that, in DFA induction, already as a result of a single deterministic merge of two nodes, divergence of randomness deficiency and MDL code can occur, which shows why the applications of MDL to grammar induction so far have been disappointing.
Journal ArticleDOI
Ease of learning explains semantic universals.
TL;DR: This work measures ease of learning using tools from machine learning and analyzes universals in a domain of function words (quantifiers) and content words (color terms) to provide strong evidence that semantic universals across both function andcontent words reflect simplicity as measured by ease oflearning.
Journal ArticleDOI
Discovering Dependencies via Algorithmic Mutual Information: A Case Study in DNA Sequence Comparisons
TL;DR: This work applies a heuristic version of the newly proposed algorithmic significance method to one of the main problems in DNA and protein sequence comparisons: the problem of deciding whether observed similarity between sequences should be explained by their relatedness or by the mere presence of some shared internal structure.
Proceedings Article
Self-Motivated Development Through Rewards for Predictor Errors / Improvements
TL;DR: The author’s old basic principles for doing so: a reinforcement learning (RL) controller is rewarded whenever its action sequences result in predictor errors or, more generally, predictor improvements are reviewed.
Journal ArticleDOI
The equiprobability bias from a mathematical and psychological perspective.
Nicolas Gauvrit,Kinga Morsanyi +1 more
TL;DR: In the present paper, it is shown that the equiprobability bias is actually not the result of a conceptual error about the definition of randomness, and on the contrary, the mathematical theory ofrandomness does imply uniformity.
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.