Kolmogorov Complexity and Solovay Functions

Laurent Bienvenu; Rod Downey

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arXiv · 0902.1041

Kolmogorov Complexity and Solovay Functions

Laurent Bienvenu·Rod Downey

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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-Löf randomness and K-triviality.

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BibTeX RIS

Laurent Bienvenu, Rod Downey. 2009-02-06. Kolmogorov Complexity and Solovay Functions. https://arxiv.org/abs/0902.1041

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