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An Introduction to Kolmogorov Complexity and Its Applications Hardcover – Feb 27 1997

5.0 out of 5 stars 6 customer reviews

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Hardcover, Feb 27 1997
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Product Details

  • Hardcover: 637 pages
  • Publisher: Springer; 2nd ed. edition (Feb. 27 1997)
  • Language: English
  • ISBN-10: 0387948686
  • ISBN-13: 978-0387948683
  • Product Dimensions: 18.5 x 3.7 x 24.4 cm
  • Shipping Weight: 1.3 Kg
  • Average Customer Review: 5.0 out of 5 stars 6 customer reviews
  • Amazon Bestsellers Rank: #1,666,139 in Books (See Top 100 in Books)
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Product Description

Review

"This is a great book. The other extant literature on Kolmogorov complexity is scattered, in need of translation, or otherwise hard to access. This book puts at all in one place in a readable, enjoyable style. In this second edition, the authors have added many new results that have been proven since the first edition was published in 1993." -- ACM's Computing Reviews

...provides a stimulating and welcome presentation that theory which deals with the quantity of information in individual objects...this book should be considered a must read for researchers and practitioners interested in maintaining an awareness of theories important to the advancement in finance. -- Randall. B. Caldwell, Journal of Computational Intelligence, FRANCE

From the Back Cover

Written by two experts in the field, this book is ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. It 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, as well as a great deal of new material not included in the first edition.

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Top Customer Reviews

Format: Hardcover Verified Purchase
So far this has been a great introduction to the subject. Particularly, I like how much of the prerequisite mathematics and background knowledge is introduced in the "Preliminaries" section. This allows the reader to fill in the gaps she may have in her knowledge, so that she may understand the concepts explored and described throughout the book. It also standardizes the notations throughout, so that readers with different backgrounds and familiar notations can engage with the material. In a sense, for an educated person who is comfortable with quantitative approaches to questions and has some basic understanding of different ideas of mathematics at a undergraduate/advanced high school level, this book is self-contained. It is also thorough, readable, and the study questions at the end of each section provide different challenges for different readers. Overall, I would highly recommend this book to someone interested in various areas such as theory of induction, statistics, the AIXI model of AGI, and general computer science and mathematics.
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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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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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