NE Is Not NP Turing Reducible to Nonexponentially 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| ≤ 2 c 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) = n , where Padding(NP, g(n)) is class of all languages LB = {s10 g(|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 Nonexpoentially 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≤n| ≤ 2nc for infinitely many integers n). Our result implies NE 6⊆...
متن کاملApproximable Sets Universitt at Karlsruhe
Much structural work on NP-complete sets has exploited SAT's d-self-reduci-bility. In this paper we exploit the additional fact that SAT is a d-cylinder to show that NP-complete sets are p-superterse unless P = NP. In fact, every set that is NP-hard under polynomial-time n o(1)-tt reductions is p-superterse unless P = NP. In particular no p-selective set is NP-hard under polynomial-time n o(1)-...
متن کاملP-Selective Sets, and Reducing Search to Decision vs. Self-Reducability
We obtain several results that distinguish self-reducibility of a language L with the question of whether search reduces to decision for L. These include: (i) If NE 6 = E, then there exists a set L in NP ? P such that search reduces to decision for L, search does not nonadaptively reduces to decision for L, and L is not self-reducible. 1 (ii) If UE 6 = E, then there exists a language L 2 UP ? P...
متن کاملSeparating the Notions of Self- and Autoreducibility
Recently Glaÿer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question whether all PSPACE-complete (NPcomplete) languages...
متن کاملVery Sparse Leaf Languages
Unger studied the balanced leaf languages defined via poly-logarithmically sparse leaf pattern sets. Unger shows that NP-complete sets are not polynomial-time many-one reducible to such balanced leaf language unless the polynomial hierarchy collapses to Θp2 and that Σ p 2-complete sets are not polynomial-time bounded-truth-table reducible (respectively, polynomial-time Turing reducible) to any ...
متن کامل