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An Introduction to Kolmogorov Complexity and Its Applications Hardcover – Feb 27 1997
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"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
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
* 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]--This text refers to an alternate Hardcover edition.
Inside This Book(Learn More)
Top Customer Reviews
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.
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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