Automatic Kolmogorov complexity, normality, and finite-state dimension revisited

Automatic Kolmogorov Complexity and Normality Revisited

It is well known that normality (all factors of given length appear in an infinite sequence with the same frequency) can be described as incompressibility via finite automata. Still the statement and proof of this result as given by Becher and Heiber [4] in terms of “lossless finite-state compressors” do not follow the standard scheme of Kolmogorov complexity definition (the automaton is used f...

Kolmogorov Complexity and Hausdorff Dimension

Constructive dimension equals Kolmogorov complexity

We derive the coincidence of Lutz’s constructive dimension and Kolmogorov complexity for sets of infinite strings from Levin’s early result on the existence of an optimal left computable cylindrical semi-measure M via simple calculations.

Resource-Bounded Kolmogorov Complexity Revisited

We take a fresh look at CD complexity, where CD t (x) is the smallest program that distinguishes x from all other strings in time t(jxj). We also look at a CND complexity, a new nondeterministic variant of CD complexity. We show several results relating time-bounded C, CD and CND complexity and their applications to a variety of questions in computational complexity theory including: Showing ho...

Human Visual Perception and Kolmogorov Complexity: Revisited

Experiments have shown [2] that we can only memorize images up to a certain complexity level, after which, instead of memorizing the image itself, we, sort of, memorize a probability distribution in terms of which this image is “random” (in the intuitive sense of this word), and next time, we reproduce a “random” sample from this distribution. This random sample may be different from the origin...