Kolmogorov Complexity and Solovay Functions
Solovay (1975) 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 $K(x) \leq f(x)+O(1)$ for all~$x$ and $f(x) \leq K(x)+O(1)$ 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.
Algorithmic randomness
Kolmogorov complexity
K-triviality
147-158
Regular Paper
Laurent
Bienvenu
Laurent Bienvenu
Rod
Downey
Rod Downey
10.4230/LIPIcs.STACS.2009.1810
Creative Commons Attribution-NoDerivs 3.0 Unported license
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