Kolmogorov Complexity and Solovay Functions

Details Kolmogorov Complexity and Solovay Functions Kolmogorov Complexity and Solovay Functions

2009-02-06

arxiv.org/abs/0902.1041v1

26th International Symposium on Theoretical Aspects of Computer Science STACS 2009 (2009) 147-158

Computer Science

Computational Complexity

Scientific paper

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.

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