Separating NE from Some Nonuniform Nondeterministic Complexity Classes

Authors

Bin Fu, The University of Texas Rio Grande Valley
Ansheng Li, The University of Texas Rio Grande Valley
Liyu Zhang, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

2011

Abstract

We investigate the question whether NE can be separated from the reduction closures of tally sets, sparse sets and NP. We show that (1) NE 6 ⊆ RNP no(1) −T (TALLY); (2)NE 6 ⊆ RSN m (SPARSE); and (3) NE 6 ⊆ PNP nk −T /nk 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.

Comments

Original published version available at https://doi.org/10.1007/s10878-010-9327-5

Recommended Citation

Fu, B., Li, A. & Zhang, L. Separating NE from some nonuniform nondeterministic complexity classes. J Comb Optim 22, 482–493 (2011). https://doi.org/10.1007/s10878-010-9327-5

Publication Title

Journal of Combinatorial Optimization

DOI

10.1007/s10878-010-9327-5