Sparse sets in NP-P: EXPTIME versus NEXPTIME

Abstract

This paper investigates the structural properties of sets in NP-P and shows that the computational difficulty of lower density sets in NP depends explicitly on the relations between higher deterministic and nondeterministic time-bounded complexity classes. The paper exploits the recently discovered upward separation method, which shows for example that there exist sparse sets in NP-P if and only if EXPTIME ≠ NEXPTIME. In addition, the paper uses relativization techniques to determine logical possibilities, limitations of these proof techniques, and exhibits one of the first natural structural differences between relativized NP and CoNP.