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 sparation method, which shows for example that there exist sparse sets in NP-P if and only if EXPTIME $\neq$ NEXPTIME. In addition, the paper uses relativization techniques to determine logical possibilities, limitations of these proof techniques, and, for the first time, to exhibit structural differences between relativized NP and CoNP.
Recommendations
On reductions of NP sets to sparse sets
Ogiwara and Watanabe showed that if SAT is bounded truth-table reducible to a sparse set, then P = NP. In this paper we simplify their proof, strengthen the result and use it to obtain several new results. Among the new results are the following:*...
Splitting NP-Complete Sets
We show that a set is m-autoreducible if and only if it is m-mitotic. This solves a long-standing open question in a surprising way. As a consequence of this unconditional result and recent work by Glaßer et al., complete sets for all of the following ...