"Extremely clear monograph on algorithmic information theory. Contains discussion of some interesting philosophical questions surrounding the meaning of andomness, as well as notion of randomness in physics and the information content of mathematical knowledge." J. Casti, Five More Golden Rules, Wiley, New York, 2000, p. 262.

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

Klappentext

The book presents in a mathematical clear way the fundamentals of algorithmic information theory and a few selected applications. This 2nd edition presents new and important results obtained in recent years: the characterization of computable enumerable random reals, the construction of an Omega Number for which ZFC cannot determine any digits, and the first successful attempt to compute the exact values of 64 bits of a specific Omega Number. Finally, the book contains a discussion of some interesting philosophical questions related to randomness and mathematical knowledge.

"Professor Calude has produced a first-rate exposition of up-to-date work in information and randomness." D.S. Bridges, Canterbury University, co-author, with Errett Bishop, of Constructive Analysis;

"The second edition of this classic work is highly recommended to anyone interested in algorithmic information and randomness." G.J. Chaitin, IBM Research Division, New York, author of Conversations with a Mathematician;

"This book is a must for a comprehensive introduction to algorithmic information theory and for anyone interested in its applications in the natural sciences." K. Svozil, Technical University of Vienna, author of Randomness & Undecidability in Physics

Inhalt
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.