Random-Self-Reducibility of Complete Sets
Abstract
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 ${\text{MOD}}_m {\text{P}}$ are random-self-reducible.
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Copyright © 1993 © Society for Industrial and Applied Mathematics.
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Submitted: 29 January 1991
Accepted: 7 July 1992
Published online: 31 July 2006
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