separating ne from some nonuniform nondeterministic complexity classes

State University of New York,; Department of Computer Science and EngineeringWe investigate the question whether NE can be separated from the reduction closures of tally sets, sparse sets and NP. We show that (1)NE ⊈ R no(1) NP-T (TALLY); (2) NE ⊈ Rm SN (SPARSE); and (3) NE ⊈ PnkT /nkNP for all k≥1. Result (3) extends a previous result by Mocas to nonuniform reductions. We also investigate how different an NE-hard set is from an NP-set. We show that for any NP subset A of a many-one-hard set H for NE, there exists another NP subset A′ of H such that A′ ⊇ A and A′-A is not of sub-exponential density. © 2009 Springer Berlin Heidelberg