On the robustness of ALMOST-R

We study the classes of the form ALMOST-R, for R a reducibility. This includes, among others, the classes BPP, P, and PH. We give a characterization of this classes in terms of reductions to n-random languages, a subclass of algorithmically random languages. Also, we give a characterization of classes of the form ALMOST-R in terms of resource bounded measure, for R reductions of a restricted kind.Postprint (updated version

On the robustness of ALMOST-R

We study the classes of the form ALMOST-R, for R a reducibility. This includes, among others, the classes BPP, P, and PH. We give a characterization of this classes in terms of reductions to n-random languages, a subclass of algorithmically random languages. Also, we give a characterization of classes of the form ALMOST-R in terms of resource bounded measure, for R reductions of a restricted kind

On the Robustness of ALMOST-R

We study the classes of the form ALMOST-R, for R a reducibility. This includes, among others, the classes BPP, P and PH. We give a characterization of these classes in terms of reductions to n-random languages, a subclass of algorithmically random languages. We also discuss the possibility of characterizing the classes ALMOST-R in terms of resource bounded measure. Supported in part by the National Science Foundation under Grant CCR-9302057. y Supported by a Spanish Government Grant FPI PN90 and by DGICYT project PB94-- 0564. This work was done while visiting the University of California, Santa Barbara. 1 Introduction Given a reducibility R, the class ALMOST-R is defined as the class of languages A such that R \Gamma1 (A) has Lebesgue probability 1. The "ALMOST-R" formalism, studied for instance in [Bo94] and [BLW94], provides characterizations of some interesting complexity classes, among others, ALMOST- P m = P [Am86], P = ALMOST- P btt [TB91], BPP = ALMOST- P T ([Am8..