Information and Randomness: An Algorithmic Perspective / Edition 2by Cristian S. Calude
Pub. Date: 11/11/2002
Publisher: Springer Berlin Heidelberg
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.
- Springer Berlin Heidelberg
- Publication date:
- Texts in Theoretical Computer Science. An EATCS Series
- Edition description:
- 2nd ed. 2002
- Product dimensions:
- 9.21(w) x 6.14(h) x 1.06(d)
Table of Contents
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I stumbled over this (lovely) book a little by accident. As I kept reading, my enthusiasm for the book gradually increased. While the book is addressed perhaps more to students in computation and in CS, it is very attractive also as a text to be used in mainstream mathematics, and in probability theory. It begins with a new look at the classical Kolmogorov construction of measures on infinite product spaces, and asks for explicit ways of labeling them with a class of certain concrete numerical functions. Then it moves onto noiseless coding theory (from communications science), but it stays rooted firmly in classical ideas from Shannon-Kolmogorov communication and information theory. It is indeed pleasing to see that God still plays dice, not only in quantum theory, but also in such classical areas of math as in number theory. From the foreword: ¿¿putting Shannon¿s information theory and Turing¿s computability theory into a cocktail shaker, and shaking vigorously¿¿ The book is a second edition 2002, with a number of attractive additions to the first edition from 1994. It will likely work equally well in a course, as for self-study. The main portion in the book focuses on classical and modern topics in computability, and its connections to randomness; covering concrete halting problems, chaos, cellular automata, algorithms, and their complexity. Palle Jorgensen, October 2004.