Refinment of the "up to a constant" ordering using contructive co-immunity and alike. Application to the Min/Max hierarchy of Kolmogorov complexities.

Marie Ferbus-Zanda (1) , Serge Grigorieff (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We introduce orderings between total functions f,g: N -> N which refine the pointwise "up to a constant" ordering <=cte and also insure that f(x) is often much less thang(x). With such orderings, we prove a strong hierarchy theorem for Kolmogorov complexities obtained with jump oracles and/or Max or Min of partial recursive functions. We introduce a notion of second order conditional Kolmogorov complexity which yields a uniform bound for the

Mots clés: Logic; Computer Science; Algorithmic Information Theory; Kolmogorov Complexity; Recursion Theory

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]; Complexité [cs.CC]

Marie Ferbus-Zanda, Serge Grigorieff. Refinment of the "up to a constant" ordering using contructive co-immunity and alike. Application to the Min/Max hierarchy of Kolmogorov complexities.. 2007. ⟨hal-00201625⟩