NE is not NP Turing Reducible to Nonexpoentially Dense NP Sets
نویسنده
چکیده
A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of NPT(NP) ∩ P/Poly. In this paper, we show that NE 6⊆ NPT(NP ∩ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c > 0, |A≤n| ≤ 2nc for infinitely many integers n). Our result implies NE 6⊆ NPT(padding(NP, g(n))) for every time constructible super-polynomial function g(n) such as g(n) = ndlogdlog nee, where Padding(NP, g(n)) is class of all languages LB = {s10g(|s|)−|s|−1 : s ∈ B} for B ∈ NP. We also show NE 6⊆ NPT(Ptt(NP) ∩ TALLY).
منابع مشابه
NE Is Not NP Turing Reducible to Nonexponentially Dense NP Sets
A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of NPT(NP) ∩ P/Poly. In this paper, we show that NE 6⊆ NPT(NP ∩ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c > 0, |A| ≤ 2 c for infinitely many integers n). Our result implies NE 6⊆ N...
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