期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2003
卷号：2003
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We study the question of whether the class DisNP of disjoint pairs (A, B) of NP-sets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provides additional evidence for the existence of P-inseparable disjoint NP-pairs. We construct an oracle relative to which the class of disjoint NP-pairs does not have a complete pair, an oracle relative to which optimal proof systems exist, hence complete pairs exist, but no pair is NP-hard, and an oracle relative to which complete pairs exist, but optimal proof systems do not exist.
