情報とランダム性:アルゴリズム的観点(第2版)<br>Information and Randomness : An Algorithmic Perspective. Forew. by Gregory J. Chaitin and Arto Salomaa (EATCS Monographs on Theoretical Computer Science) (New ed. 2002. XVI, 240 p. 24 cm)

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情報とランダム性:アルゴリズム的観点(第2版)
Information and Randomness : An Algorithmic Perspective. Forew. by Gregory J. Chaitin and Arto Salomaa (EATCS Monographs on Theoretical Computer Science) (New ed. 2002. XVI, 240 p. 24 cm)

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  • 製本 Hardcover:ハードカバー版/ページ数 238 p.
  • 商品コード 9783540434665

基本説明

Presents in a mathematically clear way the fundamentals of algorithmic information theory and a few selected applications to mathematical logic.

Full 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.

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.