On relativized exponential and probabilistic complexity classes
Information and Control
On polynomial-time bounded truth-table reducibility of NP sets to sparse sets
SIAM Journal on Computing
Almost-everywhere complexity hierarchies for nondeterministic time
Theoretical Computer Science
Measure, Stochasticity, and the Density of Hard Languages
SIAM Journal on Computing
An application of the translational method
Mathematical Systems Theory
With Quasilinear Queries EXP is not Polynomial Time Turing Reducible to Sparse Sets
SIAM Journal on Computing
Separating classes in the exponential-time hierarchy from classes in PH
Theoretical Computer Science
Separating Nondeterministic Time Complexity Classes
Journal of the ACM (JACM)
On the Cutting Edge of Relativization: The Resource Bounded Injury Method
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Two theorems on random polynomial time
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Unconditional Lower Bounds against Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Separating NE from Some Nonuniform Nondeterministic Complexity Classes
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
A hierarchy for nondeterministic time complexity
Journal of Computer and System Sciences
Online learning and resource-bounded dimension: winnow yields new lower bounds for hard sets
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Dimension, halfspaces, and the density of hard sets
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
| Hi-index | 0.00 |
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 ⊈ NPT (NP∩ Nonexponentially-Dense-Class, where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c0, |A≤n}| ≤ 2nc for infinitely many integers n). Our result implies NE ⊈ NPT (padding(NP, g(n))) for every time constructible super-polynomial function g(n) such as g(n)=n⌈log⌈log n⌉⌉, where Padding(NP, g(n)) is class of all languages LB={s10g(|s|)−|s|−1:s∈B} for B∈NP. We also show NE ⊈ NPT(Ptt(NP) ∩ TALLY).