TR03-011 Authors: Christian Glaßer, Alan L. Selman, Samik Sengupta, Liyu Zhang

Publication: 21st February 2003 18:23

Downloads: 1624

Keywords:

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.