Representable Disjoint NP-Pairs

We investigate the class of disjoint NP-pairs under different reductions. The structure of this class is intimately linked to the simulation order of propositional proof systems, and we make use of the relationship between propositional proof systems and theories of bounded arithmetic as the main tool of our analysis. Specifically we exhibit a pair which is complete under strong reductions for all disjoint NP-pairs representable in a theory. We use these pairs to explain the simulation order of NP-pairs under these reductions. As corollaries we also get simplified proofs of results obtained earlier in [3] and [5].