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An Introduction to Kolmogorov Complexity and Its Applications (Texts in Computer Science) 3rd ed. 2008 Edition

5.0 out of 5 stars 8 customer reviews
ISBN-13: 978-0387339986
ISBN-10: 0387339981
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Product Details

  • Series: Texts in Computer Science
  • Hardcover: 792 pages
  • Publisher: Springer; 3rd ed. 2008 edition (November 21, 2008)
  • Language: English
  • ISBN-10: 0387339981
  • ISBN-13: 978-0387339986
  • Product Dimensions: 7 x 1.7 x 9.2 inches
  • Shipping Weight: 3.2 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #492,874 in Books (See Top 100 in Books)

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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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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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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
to understand it. This book is intended for serious students of computer science or those who have some similar training - it is definitely set up as a textbook. However, that being said, if you have the background the authors' delivery is fist-class and very clear.
The reviews below give more than enough information so I won't belabour the Kolmogorov complexity here. Suffice it to say you won't find the subject detailed more fully in any other reference work in existence today.
However, this book does need to be revised and updated. There has been a lot of development in the field and the sections overviewing Solomonoff's work, in particular, could be expanded. Also, I found it hard to believe that nothing about the 'philosophical' importance of the whole induction question - this is at the core of many very important questions and should not be treated trivially.
There should also be some overview of two other areas that, in combination with the theory outlined in this text, are starting to form the nexus of a "new kind of science" (definitely not Wolfram's pathetic attempt). I refer to some information regarding non-classical logical systems as well as anticipatory computing systems. Both will, I predict, become core areas in addition to extensions to Kolmogorov/Chaitin complexity in the future.
All textbooks should be as clear and concise as this example.
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