On reducibility and symmetry of disjoint NP-Pairs

Abstract

We consider some problems about pairs of disjoint NP sets. The theory of these sets with a natural concept of reducibility is, on the one hand, closely related to the theory of proof systems for propositional calculus, and, on the other, it resembles the theory of NP completeness. Furthermore, such pairs are important in cryptography.A mong others, we prove that the Broken Mosquito Screen pair of disjoint NP-sets can be polynomially reduced to Clique-Coloring pair and thus is polynomially separable and we show that the pair of disjoint NP-sets canonically associated with the Resolution proof system is symmetric.