Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
Journal of Computer and System Sciences
An O(nlog log n) learning algorithm for DNF under the uniform distribution
Journal of Computer and System Sciences
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
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
Uniform-distribution attribute noise learnability
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Efficient algorithms in computational learning theory
Efficient algorithms in computational learning theory
Note: Improved hardness amplification in NP
Theoretical Computer Science
Circuit lower bounds for Merlin-Arthur classes
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the (im)possibility of non-interactive correlation distillation
Theoretical Computer Science
If NP Languages are Hard on the Worst-Case, Then it is Easy to Find Their Hard Instances
Computational Complexity
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
An invariance principle for polytopes
Proceedings of the forty-second ACM symposium on Theory of computing
Hardness amplification within NP against deterministic algorithms
Journal of Computer and System Sciences
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Query complexity in errorless hardness amplification
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Submodular functions are noise stable
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
A stronger LP bound for formula size lower bounds via clique constraints
Theoretical Computer Science
On derandomization and average-case complexity of monotone functions
Theoretical Computer Science
An invariance principle for polytopes
Journal of the ACM (JACM)
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In this paper we investigate the following question: if NP is slightly hard on average, is it very hard on average? We give a positive answer: if there is a function in NP which is infinitely often balanced and (1 - 1/poly(n))-hard for circuits of polynomial size, then there is a function in NP which is infinitely often (1/2 + n-1/2+ε)-hard for circuits of polynomial size. Our proof technique is to generalize the Yao XOR Lemma, allowing us to characterize nearly tightly the hardness of a composite function g(f(x1),....,f(xn)) in terms of: (i) the original hardness of f, and (ii) the expected bias of the function g when subjected to random restrictions. The computational result we prove essentially matches an information-theoretic bound.