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...

On provably disjoint NP-pairs

In this paper we study the pairs (U, V ) of disjoint NP-sets representable in a theory T of Bounded Arithmetic in the sense that T proves U ∩ V = ∅. For a large variety of theories T we exhibit a natural disjoint NP-pair which is complete for the class of disjoint NP-pairs representable in T . This allows us to clarify the approach to showing independence of central open questions in Boolean co...

Representable Disjoint NP-Pairs

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 ...

Canonical Disjoint NP-Pairs of Propositional Proof Systems

We prove that every disjoint NP-pair is polynomial-time, many-one equivalent to the canonical disjoint NP-pair of some propositional proof system. Therefore, the degree structure of the class of disjoint NP-pairs and of all canonical pairs is identical. Secondly, we show that this degree structure is not superficial: Assuming there exist P-inseparable disjoint pairs, there exist intermediate di...