An Introduction to Kolmogorov Complexity and Its Applications

Ming Li, Paul M.B. Vitányi

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English

Springer-Verlag New York Inc.
25 November 2014

Information theory; Coding theory & cryptology; Applied mathematics; Algorithms & data structures; Mathematical theory of computation

Series: Texts in Computer Science

“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 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 computerscience. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, Kolmogorov–Loveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.

By: Ming Li, Paul M.B. Vitányi
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: 3rd ed. 2008
Dimensions: Height: 254mm, Width: 178mm, Spine: 41mm
Weight: 1.532kg
ISBN: 9781489984456
ISBN 10: 1489984453
Series: Texts in Computer Science
Pages: 792
Publication Date: 25 November 2014
Audience: Professional and scholarly , Undergraduate
Replaced By: 9783030112974
Format: Paperback
Publisher's Status: Active

Preliminaries.- Algorithmic Complexity.- Algorithmic Prefix Complexity.- Algorithmic Probability.- Inductive Reasoning.- The Incompressibility Method.- Resource-Bounded Complexity.- Physics, Information, and Computation.

Reviews for An Introduction to Kolmogorov Complexity and Its Applications

"From the reviews of the second edition: ""We are indeed in the information age and the scientific exploration of information and the laws that govern its behavior has taken center stage in the dramatic development of sciences. Kolmogorov complexity is a central concept and a powerful tool in the understanding of the quantitative nature of information and its processing and transmission. Li and Vitanyi's book beautifully captures the elegance of these ideas, their relevance to more of computer science and their theoretical as well as practical applications. The basic concepts of Kolmogorov complexity should be understood by any technically educated person, and they should be studied by all computer scientists. Li and Vitanyi have provided an ideal book for the exploration of a deep, beautiful and important part of the computer science."" Juris Hartmanis, (Turing Award Winner 1993), NSF, Washington D.C. ""Special attention is paid to the theory underlying inductive inference and its potential applications. The book is likely to remain the standard treatment of Kolmogorov complexity for a long time."" Jorma J. Rissanen, IBM Research, California ""The book of Li and Vitanyi is unexcelled."" Ray J. Solomonoff, Oxbridge Research, Cambridge, Massachusetts ""The book is outstanding . . . the authors did their job unbelievably well...necessary reading for all kinds of readers from undergraduate students to top authorities in the field."" Vladimir A. Uspensky and Alexander K. Shen, Journal of Symbolic Logic ""It is clear that this book will become 'the' Kolmogorov complexity book."" Marius Zimand, Mathematical Reviews From the reviews of the third edition: ""Kolmogorov complexity, algorithmic information theory, minimum description length, and other information-based disciplines have experienced a phenomenal explosion in the last decade. … is thisthird edition worth reading? Yes, it is. The authors have added an extra 204 pages, distributed throughout the book … . Eight new figures were also added. Most impressively, 301 new references were added, bringing the total to 820. … It is sure to maintain its reputation … ."" (Jacques Carette, ACM Computing Reviews, April, 2009)"