Separating NE from some nonuniform nondeterministic complexity classes

Bin Fu (), Angsheng Li () and Liyu Zhang ()
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Bin Fu: University of Texas-Pan American
Angsheng Li: Chinese Academy of Sciences
Liyu Zhang: University of Texas at Brownsville

Journal of Combinatorial Optimization, 2011, vol. 22, issue 3, No 13, 482-493

Abstract: 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) $\mathrm{NE}\not\subseteq R^{\mathrm{NP}}_{n^{o(1)}-T}(\mathrm{TALLY})$ ; (2) $\mathrm{NE}\not\subseteq R^{SN}_{m}(\mathrm{SPARSE})$ ; (3) $\mathrm{NEXP}\not\subseteq \mathrm{P}^{\mathrm{NP}}_{n^{k}-T}/n^{k}$ for all k≥1; and (4) $\mathrm{NE}\not\subseteq \mathrm{P}_{btt}(\mathrm{NP}\oplus\mathrm{SPARSE})$ . 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.

Keywords: NE; NEXP; Nonuniform complexity class; Separation; Complexity (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10878-010-9327-5

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