Texts in Computer Science

An Introduction to Kolmogorov Complexity and Its Applications

Authors: Li, Ming, Vitanyi, Paul

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About this Textbook

Briefly, we review the basic elements of computability theory and prob­ ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo­ rithmic complexity theory. The theory of Martin-Lof tests for random­ ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion­ theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor­ mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup­ poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).

Table of contents (8 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4757-2606-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Kolmogorov Complexity and Its Applications
Authors
Series Title
Texts in Computer Science
Copyright
1997
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-2606-0
DOI
10.1007/978-1-4757-2606-0
Series ISSN
1868-0941
Edition Number
2
Number of Pages
XX, 637
Number of Illustrations and Tables
8 b/w illustrations
Additional Information
Originally published in the series: Texts, Monographs Computer Science
Topics