A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
On the power of two-point based sampling
Journal of Complexity
On the degree of polynomials that approximate symmetric Boolean functions (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Rounds in communication complexity revisited
SIAM Journal on Computing
Communication complexity and quasi randomness
SIAM Journal on Discrete Mathematics
The computational complexity of universal hashing
Theoretical Computer Science - Special issue on structure in complexity theory
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
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
Constant depth circuits, Fourier transform, and learnability
Journal of the ACM (JACM)
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
Communication complexity
The average sensitivity of bounded-depth circuits
Information Processing Letters
The BNS-chung criterion for multi-party communication complexity
Computational Complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Lower Bounds for Lovász-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity
SIAM Journal on Computing
Discrepancy and the Power of Bottom Fan-in in Depth-three Circuits
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth 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
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Separating ${AC}^0$ from Depth-2 Majority Circuits
SIAM Journal on Computing
Constant-Depth circuits for arithmetic in finite fields of characteristic two
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Hadamard tensors and lower bounds on multiparty communication complexity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Separating deterministic from nondeterministic nof multiparty communication complexity
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The multiparty communication complexity of set disjointness
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We exhibit an explicit function f : {0, 1}n →{0, 1} that can be computed by a nondeterministic number-on-forehead protocol communicating O(logn) bits, but that requires nΩ(1) bits of communication for randomized number-on-forehead protocols with k = δ·logn players, for any fixed δ k n. We also show that for any k = A ·loglogn the above function f is computable by a small circuit whose depth is constant whenever A is a (possibly large) constant. Recent results again give such functions but only when the number of players is k n.