Features
- Cover Type: Hard Cover with 637 pages
- Published by: Springer; 2nd ed. edition February 27, 1997
- Written in: English
- ISBN 10 Number: 0387948686
- ISBN 13 Number: 978-0387948683
-
Book Dimensions:
10.2 x 7 x 1.6 inches
- Weighs: 2.9 pounds
ACM's Computing Reviews
"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."
Randall. B. Caldwell, Journal of Computational Intelligence, FRANCE
provides a stimulating and welcome presentation that theory which deals with the quantity of information in individual objectsthis book should be considered a must read for researchers and practitioners interested in maintaining an awareness of theories important to the advancement in finance.
Reader Reviews
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. The discussion of randomness in the Diophantine equations; it is shown that the set of indices of the Diophantine equations with infinitely many different solutions is not recursively enumerable; with the initial segment of length n in the characteristic sequence having Kolmogorov complexity n. 9. The discussion on algorithmic probability, especially the test for randomness by martingales. 10. The Solomonoff theory of prediction and its ability to solve the problem of induction. 11. The treatment of Pac-learning and the resultant formalization of Occam's razor. 12. The discussion of compact routing; the optimal space to represent routing schemes in communication networks on the average for all static networks. 13. Computational complexity and its connection to resource-bounded complexity. 14. The notion of logical depth, i.e. the time required by a universal computer to compute the object from its compressed original description. 15. The connection between algorithmic complexity and Shannon's entropy. 16. The discussion on reversible computation, i.e. logically reversible computers that do not dissipate heat. 17. The treatment of information distance, i.e. for two strings, the minimal quantity of information sufficient to translate from one to the other.
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