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Information and Randomness: An Algorithmic Perspective (Lecture Notes in Computer Science)

By Cristian Calude

Publisher:

 

Springer

Number Of Pages:

 

240

Publication Date:

 

1994-01

ISBN-10 / ASIN:

 

3540574565

ISBN-13 / EAN:

 

9783540574569

Product Description:

"Algorithmic information theory (AIT) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously", says G.J. Chaitin, one of the fathers of this theory of complexity and randomness, which is also known as Kolmogorov complexity. It is relevant for logic (new light is shed on Gödel's incompleteness results), physics (chaotic motion), biology (how likely is life to appear and evolve?), and metaphysics (how ordered is the universe?). 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.

Summary: Classical ideas with modern use.

Rating: 5

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.

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Rating:
2.5 out of 5 by Book123