© 2019

An Introduction to Kolmogorov Complexity and Its Applications


Part of the Texts in Computer Science book series (TCS)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Ming Li, Paul Vitányi
    Pages 1-99
  3. Ming Li, Paul Vitányi
    Pages 101-199
  4. Ming Li, Paul Vitányi
    Pages 201-260
  5. Ming Li, Paul Vitányi
    Pages 261-343
  6. Ming Li, Paul Vitányi
    Pages 345-448
  7. Ming Li, Paul Vitányi
    Pages 449-545
  8. Ming Li, Paul Vitányi
    Pages 547-622
  9. Ming Li, Paul Vitányi
    Pages 623-761
  10. Back Matter
    Pages 763-834

About this book


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.

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.


Shannon Symbol algorithms artificial intelligence communication complexity computer computer science information information theory intelligence learning learning theory logic statistics

Authors and affiliations

  1. 1.University of WaterlooWaterlooCanada
  2. 2.Centrum voor Wiskunde en Informatica (CWI)AmsterdamThe Netherlands

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.


Textbook & Academic Authors Association 2020 McGuffey Longevity Award Winner!

The judges said:

"An Introduction to Kolmogorov complexity and Its Applications has been an outstanding textbook and comprehensive reference for on information complexity for over twenty years. This new edition continues that tradition by laying a terrific foundation in the early chapters for the more advanced theories and concepts that follow. Each new theorem and corollary flows naturally and logically from what came before."

Bibliographic information