Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of

The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. T

Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropria

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshop

"Algorithmic information theory (AIT) is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking