On the Random-Self-Reducibility of Complete Sets

Abstract. In this paper, we generalize the previous formal de nitions of random-self-reducibility. We show that, even under our very general de nition, 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 MODmP are random-self-reducible. Key words. random-self-reductions, complexity classes, interactive proof systems, program checkers AMS(MOS) subject classi cations. 68Q05, 68Q15

• Type: Conference
• Year: 1991
• Where: COCO
• Authors: Joan Feigenbaum, Lance Fortnow
• Keywords: Algorithms, COCO 1991, Hierarchy Collapses, Interactive Proof Systems, Polynomial Hierarchy