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.
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Fu, B., Li, A., Zhang, L. (2009). Separating NE from Some Nonuniform Nondeterministic Complexity Classes. In: Ngo, H.Q. (eds) Computing and Combinatorics. COCOON 2009. Lecture Notes in Computer Science, vol 5609. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02882-3_48
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DOI: https://doi.org/10.1007/978-3-642-02882-3_48
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