We define a new discrete version of scaled dimension and we find
connections between the scaled dimension of a string and its Kolmogorov
complexity and predictability. We give a new characterization
of constructive scaled dimension by Kolmogorov complexity, and prove
a new result about scaled dimension and prediction.
A dimension extractor is an algorithm designed to increase the effective dimension -- i.e., the computational information density -- of an infinite sequence. A constructive dimension extractor is exhibited by showing that every sequence of positive constructive dimension is Turing equivalent to a sequence of constructive strong dimension arbitrarily ... more >>>
