Finite projective spaces and intersecting hypergraphs
Combinatorica
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
n&OHgr;(logn) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom
Information Processing Letters
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
The BNS lower bound for multi-party protocols is nearly optimal
Information and Computation
Journal of Computer and System Sciences
Separating the communication complexities of MOD m and MOD p circuits
Journal of Computer and System Sciences
Representing Boolean functions as polynomials modulo composite numbers
Computational Complexity - Special issue on circuit complexity
Communication complexity
Circuits and multi-party protocols
Computational Complexity
A lower bound on the MOD 6 degree of the or function
Computational Complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
On the Weak mod m Representation of Boolean Functions
On the Weak mod m Representation of Boolean Functions
Designs, Codes and Cryptography
Pairs of codes with prescribed Hamming distances and coincidences
Designs, Codes and Cryptography
Polynomials that Sign Represent Parity and Descartes' Rule of Signs
Computational Complexity
SIAM Journal on Computing
New bounds for matching vector families
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Let f be an n-variable polynomial with positive integer coefficients, and let H = {H1, H2,..., Hm} be a set system on the n-element universe. We define a set system f(H) = {G1, G2,..., Gm} and prove that f(Hi1 ∩ Hi2 ∩... ∩ Hik) = |Gi1 ∩ Gi2 ∩ ... ∩ Gik|, for any 1 ≤ k ≤ m, where f(Hi1 ∩ Hi2 ∩... ∩Hik) denotes the value of f on the characteristic vector of Hi1 ∩ Hi2 ∩... ∩ Hik. The construction of f(H) is a straightforward polynomial-time algorithm from the set system H and the polynomial f. In this paper we use this algorithm for constructing set systems with prescribed intersection sizes modulo an integer. As a by-product of our method, some upper bounds on the number of sets in set systems with prescribed intersection sizes are extended.