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LIPIcs - Leibniz International Proceedings in Informatics. 26th International Symposium on Theoretical Aspects of Computer Science
Doi
Abstract
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)leqf(x)+O(1) for all~x and f(x)leqK(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
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