Separating NE from Some Nonuniform Nondeterministic Complexity Classes

  • Authors:

  • Bin Fu;Angsheng Li;Liyu Zhang

  • Affiliations:

  • Dept. of Computer Science, University of Texas, Pan American, USA 78539;Institute of Software, Chinese Academy of Sciences, Beijing, P.R. China;Department of Computer and Information Sciences, University of Texas at Brownsville, Brownsville, USA 78520

  • Venue:
  • COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
  • Year:
  • 2009

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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) ${\rm NE}\not\subseteq R^{{\rm NP}}_{n^{o(1)}-T}({\rm TALLY})$; (2)${\rm NE}\not\subseteq R^{SN}_m({\rm SPARSE})$; and (3) ${\rm NE}\not\subseteq {\rm P}^{{\rm NP}}_{n^k-T}/n^k$ 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.