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.
Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.147-158, 2009
https://hal.inria.fr/inria-00359056
Contributeur : Publications Loria
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Soumis le : jeudi 5 février 2009 - 14:27:58
Dernière modification le : jeudi 12 février 2009 - 15:51:40
Document(s) archivé(s) le : mardi 8 juin 2010 - 20:14:03
Laurent Bienvenu, Rod Downey. Kolmogorov Complexity and Solovay Functions. Susanne Albers and Jean-Yves Marion. 26th International Symposium on Theoretical Aspects of Computer Science STACS 2009, Feb 2009, Freiburg, Germany. IBFI Schloss Dagstuhl, pp.147-158, 2009. 〈inria-00359056〉
