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Information and Randomness

An Algorithmic Perspective

  • Textbook
  • © 2002

Overview

Authors:
  1. Cristian S. Calude

    1. Department of Computer Science, Auckland University, Auckland, New Zealand

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  • The only coherent presentation of Omega Numbers.
  • Includes supplementary material: sn.pub/extras

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XX
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  2. Mathematical Background

    • Cristian S. Calude
    Pages 1-20

  3. Noiseless Coding

    • Cristian S. Calude
    Pages 21-32

  4. Program-size

    • Cristian S. Calude
    Pages 33-52

  5. Computably Enumerable Instantaneous Codes

    • Cristian S. Calude
    Pages 53-93

  6. Random Strings

    • Cristian S. Calude
    Pages 95-146

  7. Random Sequences

    • Cristian S. Calude
    Pages 147-235

  8. Computably Enumerable Random Reals

    • Cristian S. Calude
    Pages 237-314

  9. Randomness and Incompleteness

    • Cristian S. Calude
    Pages 315-360

  10. Applications

    • Cristian S. Calude
    Pages 361-413

  11. Open Problems

    • Cristian S. Calude
    Pages 415-417

  12. Back Matter

    Pages 419-468
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Keywords

About this book

The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob­ lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom­ pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.

Reviews

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)

Authors and Affiliations

  • Department of Computer Science, Auckland University, Auckland, New Zealand

    Cristian S. Calude

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