The power of adaptiveness and additional queries in random-self-reductions

Abstract

We study random-self-reductions from a structural complexity-theoretic point of view. Specifically, we look at relationships between adaptive and nonadaptive random-self-reductions. We also look at what happens to random-self-reductions if we restrict the number of queries they are allowed to make. We show the following results:{ring operator} There exist sets that are adaptively random-self-reducible but not nonadaptively random-self-reducible. Under plausible assumptions, there exist such sets in NP. {ring operator} There exists a function that has a nonadaptive (k(n)+1)-random-self-reduction but does not have an adaptive k(n)-random-self-reduction. {ring operator} For any countable class of functions C and any unbounded function k(n), there exists a function that is nonadaptively k(n)-uniformly-random-self-reducible but is not in C/poly. This should be contrasted with Feigenbaum, Kannan, and Nisan's theorem that all nonadaptively 2-uniformly-random-self-reducible sets are in NP/poly. © 1994 Birkhäuser Verlag.