Kolmogorov Complexity and Solovay Functions
Computational Complexity
2009-02-10 v1 Information Theory
math.IT
Logic
Abstract
Solovay proved that there exists a computable upper bound f of the prefix-free Kolmogorov complexity function K such that f (x) = K(x) for infinitely many x. In this paper, we consider the class of computable functions f such that K(x) <= f (x)+O(1) for all x and f (x) <= K(x) + O(1) for infinitely many x, which we call Solovay functions. We show that Solovay functions present interesting connections with randomness notions such as Martin-L\"of randomness and K-triviality.
Keywords
Cite
@article{arxiv.0902.1041,
title = {Kolmogorov Complexity and Solovay Functions},
author = {Laurent Bienvenu and Rod Downey},
journal= {arXiv preprint arXiv:0902.1041},
year = {2009}
}