Texts in Computer Science

An Introduction to Kolmogorov Complexity and Its Applications

Authors: Li, Ming, Vitányi, Paul

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  • Develops Kolmogorov theory in detail, and outlines a wide range of illustrative applications
  • Examines major results from prominent researchers in the field
  • Details the practical application of KC in the similarity metric and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering
  • Includes new and updated material on the Miller-Yu theorem, the Gács-Kučera theorem, the Day-Gács theorem, the Lovász local lemma, and the Slepian-Wolf theorem
  • Discusses short lists computable from an input string containing the incomputable Kolmogorov complexity of the input
  • Covers topics of increasing randomness, sorting, multiset normalized information distance and normalized web distance, and conditional universal distribution
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eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-030-11298-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA in USD
  • ISBN 978-3-030-11297-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features.

This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gács-Kučera theorem, the Day-Gács theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovász local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution.

Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface.

As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.

About the authors

Dr. Paul M.B. Vitányi is a CWI Fellow at the Netherlands National Research Institute for Mathematics and Computer Science (CWI), and a Professor of Computer Science at the University of Amsterdam. Dr. Ming Li is Canada Research Chair in Bioinformatics and University Professor at the University of Waterloo, ON, Canada.

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Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-030-11298-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA in USD
  • ISBN 978-3-030-11297-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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
2019
Publisher
Springer International Publishing
Copyright Holder
Ming Li and Paul Vitányi
eBook ISBN
978-3-030-11298-1
DOI
10.1007/978-3-030-11298-1
Hardcover ISBN
978-3-030-11297-4
Series ISSN
1868-0941
Edition Number
4
Number of Pages
XXIII, 834
Number of Illustrations
1 b/w illustrations
Topics