Abstract
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 can have equivalent canonical pairs and that depending on the properties of the proof systems different scenarios for DNPP ( P ) and the reductions between the canonical pairs exist.
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