Disjoint NP-Pairs

We study the question of whether the class DisjNP 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, and 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. Key words. disjoint NP-pairs, promise problems, propositional proof systems, oracles, symmetry AMS subject classification. 68Q15 DOI. 10.1137/S0097539703425848

• Type: Conference
• Year: 2003
• Where: COCO
• Authors: Christian Glaßer, Alan L. Selman, Samik Sengupta, Liyu Zhang
• Keywords: COCO 2003, Disjoint Np-pairs, Disjoint Pair, Optimal Proof Systems