Fast moment estimation in data streams in optimal space
Proceedings of the forty-third annual ACM symposium on Theory of computing
Black-box reductions in mechanism design
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
A dichotomy for local small-bias generators
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Explicit Dimension Reduction and Its Applications
SIAM Journal on Computing
An invariance principle for polytopes
Journal of the ACM (JACM)
A PRG for lipschitz functions of polynomials with applications to sparsest cut
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Pseudorandom generators for combinatorial checkerboards
Computational Complexity
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For an $n$-variate degree–$2$ real polynomial $p$, we prove that $\E_{x\sim \mathcal{D}}[\sgn(p(x))]$ is determined up to an additive $\eps$ as long as $\mathcal{D}$ is a $k$-wise independent distribution over $\bits^n$ for $k = \poly(1/\eps)$. This gives a broad class of explicit pseudorandom generators against degree-$2$ boolean threshold functions, and answers an open question of Diakonikolas et al. (FOCS 2009).