© 2002

Information and Randomness

An Algorithmic Perspective


Table of contents

  1. Front Matter
    Pages I-XX
  2. Cristian S. Calude
    Pages 1-20
  3. Cristian S. Calude
    Pages 21-32
  4. Cristian S. Calude
    Pages 33-52
  5. Cristian S. Calude
    Pages 53-93
  6. Cristian S. Calude
    Pages 95-146
  7. Cristian S. Calude
    Pages 147-235
  8. Cristian S. Calude
    Pages 237-314
  9. Cristian S. Calude
    Pages 315-360
  10. Cristian S. Calude
    Pages 361-413
  11. Cristian S. Calude
    Pages 415-417
  12. Back Matter
    Pages 419-468

About this book


The book presents in a mathematical clear way the fundamentals of algorithmic information theory and a few selected applications. This 2nd edition presents new and important results obtained in recent years: the characterization of computable enumerable random reals, the construction of an Omega Number for which ZFC cannot determine any digits, and the first successful attempt to compute the exact values of 64 bits of a specific Omega Number. Finally, the book contains a discussion of some interesting philosophical questions related to randomness and mathematical knowledge.

"Professor Calude has produced a first-rate exposition of up-to-date work in information and randomness." D.S. Bridges, Canterbury University, co-author, with Errett Bishop, of Constructive Analysis;

"The second edition of this classic work is highly recommended to anyone interested in algorithmic information and randomness." G.J. Chaitin, IBM Research Division, New York, author of Conversations with a Mathematician;

 "This book is a must for a comprehensive introduction to algorithmic information theory and for anyone interested in its applications in the natural sciences." K. Svozil, Technical University of Vienna, author of Randomness & Undecidability in Physics


Chaitin complexity Kolmogorov complexity algorithmic information theory algorithms computability randomization discrete mathematics halting probability incompleteness information information theory logic philosophy physics random string/sequence randomness

Authors and affiliations

  1. 1.Department of Computer ScienceAuckland UniversityAucklandNew Zealand

Bibliographic information

Industry Sectors
Finance, Business & Banking


From the reviews of the second edition:

"This book, benefiting from the author’s research and teaching experience in Algorithmic Information Theory (AIT) should help to make the detailed mathematical techniques of AIT accessible to a much wider audience." (PHINEWS, Vol. 2, October 2002)