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.
