Disjoint NP-Pairs

Authors

Christian Glasser
Alan L. Selman
Samik Sengupta
Liyu Zhang, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2004

Abstract

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.

Comments

Original published version available at

Recommended Citation

Glaßer, Christian, Alan L. Selman, Samik Sengupta, and Liyu Zhang. "Disjoint NP-pairs." SIAM Journal on Computing 33, no. 6 (2004): 1369-1416. https://doi.org/10.1137/S0097539703425848

Publication Title

SIAM Journal on Computing

DOI

10.1137/S0097539703425848