Information and randomness : an algorithmic perspective
Author(s)
Bibliographic Information
Information and randomness : an algorithmic perspective
(Texts in theoretical computer science, An EATCS series)
Springer-Verlag, c2002
2nd ed., revised and extended
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
CAL||12||1(2)04068212
Note
Includes bibliographical references (p. [419]-453) and indexes
Description and Table of Contents
Description
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.
Table of Contents
1 Mathematical Background.- 2 Noiseless Coding.- 3 Program-size.- 4 Computably Enumerable Instantaneous Codes.- 5 Random Strings.- 6 Random Sequences.- 7 Computably Enumerable Random Reals.- 8 Randomness and Incompleteness.- 9 Applications.- 10 Open Problems.- Notation Index.- Name Index.
by "Nielsen BookData"