Classes of representable disjoint NP-pairs

Classes of Representable Disjoint NP - Pairs 1

For a propositional proof system P we introduce the complexity class DNPP(P ) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P . We exhibit structural properties of proof systems which make canonical NP-pairs associated with these proof systems hard or complete for DNPP(P ). Moreover, we demonstrate that non-equivalent proof systems c...

Classes of representable disjoint NP-pairs

For a propositional proof system P we introduce the complexity class DNPP(P) of all disjoint NP-pairs for which the disjointness of the pair is efficiently provable in the proof system P . We exhibit structural properties of proof systems which make canonical NP-pairs associated with these proof systems hard or complete for DNPP(P). Moreover, we demonstrate that nonequivalent proof systems can ...

Representable Disjoint NP-Pairs

Disjoint NP-Pairs

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 provi...

Disjoint NP - Pairs ( Extended

We study the question of whether the class D 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 ...