Random-Self-Reducibility of Complete Sets

This paper generalizes the previous formal definitions of random-self-reducibility. It is shown that, even under a very general definition, sets that are complete for any level of the polynomial hierarchy are not nonadaptively random-self-reducible, unless the hierarchy collapses. In particular, NP-complete sets are not nonadaptively random-self-reducible, unless the hierarchy collapses at the third level. By contrast, we show that sets complete for the classes PP and MODₘ P are random-self-reducible.