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. The basic idea is to measure
the complexity of an object by the size in bits of the smallest
program for computing it. (G. J. Chaitin)
open questions paper by Joe Miller and Andre Nies.
AIT-related software on Greg Chaitin's
Special session Computability and Randomness at TAMC07, Computability Theory at Joint Meeting of the AMS-NZMS 2007