Strong Reductions and Isomorphism of Complete Sets

Abstract

We study the structure of the polynomial-time complete sets for NP and PSPACE under strong nondeterministic polynomial-time reductions (SNP-reductions). We show the following results. -- If NP contains a p-random language, then all polynomial-time complete sets for PSPACE are SNP-isomorphic. -- If NP ∩ co-NP contains a p-random language, then all polynomial-time complete sets for NP are SNP-isomorphic.