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An Introduction to Kolmogorov Complexity and Its Applications (Texts in Computer Science) [Hardcover]

Ming Li , Paul M.B. Vitányi
5.0 out of 5 stars  See all reviews (9 customer reviews)

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Book Description

March 5, 2009 0387339981 978-0387339986 3rd ed. 2008

“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 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, Kolmogorov–Loveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.


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An Introduction to Kolmogorov Complexity and Its Applications (Texts in Computer Science) + An Introduction to Information Theory: Symbols, Signals and Noise (Dover Books on Mathematics)
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Editorial Reviews

Review

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 this third 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)

From the Back Cover

This ongoing bestseller, now in its third edition, is considered the standard reference on Kolmogorov complexity, a modern theory of information that is concerned with information in individual objects.

New key features and topics in the 3rd edition:

* New results on randomness

* Kolmogorov's structure function, model selection, and MDL

* Incompressibility method: counting unlabeled graphs, Shellsort, communication complexity

* Derandomization

* Kolmogorov complexity versus Shannon information, rate distortion, lossy compression, denoising

* Theoretical results on information distance

* The similarity metric with applications to genomics, phylogeny, clustering, classification, semantic meaning, question-answer systems

*Quantum Kolmogorov complexity

Written by two experts in the field, this book is ideal for advanced undergraduate students, graduate students, and researchers in all fields of science. It is self-contained: it contains the basic requirements from mathematics, probability theory, statistics, information theory, and computer science. Included are history, theory, new developments, a wide range of applications, numerous (new) problem sets, comments, source references, and hints to solutions of problems. This is the only comprehensive treatment of the central ideas of Kolmogorov complexity and their applications.

``Li and Vitányi have provided an ideal book for the exploration of a deep, beautiful and important part of computer science.''

-- Juris Hartmanis, Turing Award Winner 1993, Cornell University, Ithaca, NY.

``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 Vitányi 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 [Review]

``Careful and clear introduction to a subtle and deep field.''

--David G. Stork, Ricoh Innovations, California, Amazon [Review]

``THE book on Kolmogorov Complexity.''

--Lance Fortnow, University of Chicago, IL, Amazon [Review]


Product Details

  • Series: Texts in Computer Science
  • Hardcover: 792 pages
  • Publisher: Springer; 3rd ed. 2008 edition (March 5, 2009)
  • Language: English
  • ISBN-10: 0387339981
  • ISBN-13: 978-0387339986
  • Product Dimensions: 9.2 x 7 x 1.7 inches
  • Shipping Weight: 3.2 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #634,417 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
80 of 81 people found the following review helpful
5.0 out of 5 stars Biggest return for the biggest investment May 7, 2005
Format:Hardcover
This was the second-hardest book I ever read. Honestly, it took me years and years to get through it. I even had to buy a 2nd copy, because I kept getting frustrated and throwing the first copy across the room until it was destroyed. So yes, this book requires a substantial effort to read.

But the payback!! I've gotten more return on investment from this book than from any other book I've ever read. If you dilligently read and master this book, you will be able to analyze and solve problems your collegues just can't.

The basic idea behind Kolmogorov complexity is straighforward: a good measure of the complexity of an object is the length of the shortest computer program which will construct that object. From this basic idea an amazing variety of insights and powerful techniques have been developed, and this book is quite comprehensive in cataloging and explaining them.

For computer scientists and working programmers, probably the most useful result of Kolmogorov complexity would be the "Incompressibility Method", which is a powerful technique for the analysis of the runtime of algorithms. Typically, it is relatively easy to figure out what the best case or the worst case runtime of an algorithm is. Until now, it was hard to calculate the average runtime of an algorithm, because it usually involved a tricky counting problem, to enumerate all possible runs of the the algorithm and summing over them. The incompressibility method eliminates the need for doing these complicated enumerations, by letting you perform the analysis on a single run of the algorithm which is guarunteed to be representative of the average runtime of the algorithm.
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24 of 26 people found the following review helpful
5.0 out of 5 stars The only one of its kind.... September 22, 2001
Format:Hardcover
The theory of Kolmogorov complexity attempts to define randomness in terms of the complexity of the program used to compute it. The authors give an excellent overview of this theory, and even discuss some of its philosophical ramifications, but they are always careful to distinguish between mathematical rigor and philosophical speculation. And, interestingly, the authors choose to discuss information theory in physics and the somewhat radical idea of reversible computation. The theory of Kolmogorov complexity is slowly making its way into applications, these being coding theory and computational intelligence, and network performance optimization, and this book serves as a fine reference for those readers interested in these applications. Some of the main points of the book I found interesting include: 1. A very condensed but effective discussion of Turing machines and effective computability. 2. The historical motivation for defining randomness and its defintiion using Kolmogorov complexity. 3. The discussion of coding theory and its relation to information theory. The Shannon-Fano code is discussed, along with prefix codes, Kraft's inequality, the noiseless coding theorem, and universal codes for infinite source word sets. 4. The treatment of algorithmic complexity. The authors stress that the information content of an object must be intrinsic and independent of the means of description. 5. The discussion of the explicit universal randomness test. 6. The discussion (in an exercise) of whether a probabilistic machine can perform a task that is impossible on a deterministic machine. 7. The notion of incompressibility of strings. 8. Read more ›
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16 of 17 people found the following review helpful
5.0 out of 5 stars THE book on Kolmogorov Complexity October 13, 1998
Format:Hardcover
When is an object "random"? Kolmogorov (and others) argue that one could measure randomness by the shortest description, i.e. computer program, that generates it.
This simple idea leads to a beautiful mathematical theory and a powerful tool as one can show that random objects have several interesting properties.
Li and Vitanyi have written this wonderful monograph on the area covering the depth of theory and applications not seen anywhere else. They give a clear and complete descriptions of many of the important concepts in the book. I have used this book twice in teaching graduate courses on the topic.
This book is a must have for anyone interested in a serious mathematical treatment of Kolmogorov complexity.
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9 of 9 people found the following review helpful
5.0 out of 5 stars A must October 29, 2003
Format:Hardcover
The book provides all the tools needed for a productive use of the theory. Written by leading experts in the field, the book is both a fascinating introduction as well as a comprehensive reference for experts.
The authors are careful to place the development of the theory in its historical context, give a face to the main players in the field and explore frictions with other lines of thought. But the main storyline is the mathematical world of Kolmogorov complexity. Neccessary background knowledge is provided, most proofs are given and the open problems are presented. Most chapters are more or less self sufficient, making it possible to skip those that are of less relevance to you. In the later chapters much thought is given to the different fields of application.
A third edition is in the making which will include recent advances. But since the authors make new discoveries available on the web, the present edition will continue for a long time to hold a prominent place in the book shelves of many computer scientist.
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