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An Introduction to Kolmogorov Complexity and Its Applications

3rd Edition

By Ming Li , Paul M.B. Vitányi

An Introduction to Kolmogorov Complexity and Its Applications Cover Image

Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications.

Full Description

  • ISBN13: 978-0-3873-3998-6
  • 816 Pages
  • User Level: Students
  • Publication Date: March 18, 2009
  • Available eBook Formats: PDF
  • eBook Price: $84.95
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Full Description
“The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field.” Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, Kolmogorov–Loveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.
Table of Contents

Table of Contents

  1. Preliminaries.
  2. Algorithmic Complexity.
  3. Algorithmic Prefix Complexity.
  4. Algorithmic Probability.
  5. Inductive Reasoning.
  6. The Incompressibility Method.
  7. Resource
  8. Bounded Complexity.
  9. Physics, Information, and Computation.
  10. Shannon Information and Kolmogorov Complexity.
  11. Information Distance.
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