Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Results on communication complexity classes
Journal of Computer and System Sciences
A direct version of Shamir and Snir's lower bounds on monotone circuit depth
Information Processing Letters
Communication complexity
Lower bounds on arithmetic circuits via partial derivatives
Computational Complexity
A lower bound for monotone arithmetic circuits computing 0-1 permanent
Theoretical Computer Science
Some Exact Complexity Results for Straight-Line Computations over Semirings
Journal of the ACM (JACM)
Negation can be exponentially powerful
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Multi-linear formulas for permanent and determinant are of super-polynomial size
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Multilinear formulas and skepticism of quantum computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Extracting Randomness Using Few Independent Sources
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Extractors for a constant number of polynomially small min-entropy independent sources
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Disjointness Is Hard in the Multi-party Number-on-the-Forehead Model
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
On the P versus NP intersected with co-NP question in communication complexity
Information Processing Letters
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
Tensor-Rank and Lower Bounds for Arithmetic Formulas
Journal of the ACM (JACM)
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We study a new method for proving lower bounds for subclasses of arithmetic circuits. Roughly speaking, the lower bound is proved by bounding the correlation between the coefficients' vector of a polynomial and the coefficients' vector of any product of two polynomials with disjoint sets of variables. We prove lower bounds for several old and new subclasses of circuits: monotone circuits, orthogonal formulas, non-canceling formulas, and noise-resistant formulas. One ingredient of our proof is an explicit map that has exponentially small discrepancy for every partition of the input variables into two sets of roughly the same size. We give two additional applications of this explicit map: to extractors construction and to communication complexity.