P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
On Worst-Case to Average-Case Reductions for NP Problems
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Hardness amplification within NP
Journal of Computer and System Sciences - Special issue on computational complexity 2002
The complexity of constructing pseudorandom generators from hard functions
Computational Complexity
On Constructing Parallel Pseudorandom Generators from One-Way Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
On the Complexity of Hardness Amplification
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Using Nondeterminism to Amplify Hardness
SIAM Journal on Computing
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
| Hi-index | 5.23 |
We study the problem of hardness amplification in NP. We prove that if there is a balanced function in NP such that any circuit of size s(n)=2^@W^(^n^) fails to compute it on a 1/poly(n) fraction of inputs, then there is a function in NP such that any circuit of size s^'(n) fails to compute it on a 1/2-1/s^'(n) fraction of inputs, with s^'(n)=2^@W^(^n^^^2^^^/^^^3^). This improves the result of Healy et al. (STOC'04), which only achieves s^'(n)=2^@W^(^n^^^1^^^/^^^2^) for the case with s(n)=2^@W^(^n^).