Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
On the distributional complexity of disjointness
Theoretical Computer Science
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
On the degree of Boolean functions as real polynomials
Computational Complexity - Special issue on circuit complexity
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Computational complexity questions related to finite monoids and semigroups
Computational complexity questions related to finite monoids and semigroups
On Computation and Communication with Small Bias
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
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
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
A note on the power of threshold circuits
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Lower Bounds on Quantum Multiparty Communication Complexity
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
Separating ${AC}^0$ from Depth-2 Majority Circuits
SIAM Journal on Computing
Multiparty Communication Complexity and Threshold Circuit Size of AC^0
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
Quantum communication complexity of block-composed functions
Quantum Information & Computation
The multiparty communication complexity of set disjointness
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
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We study the set disjointness problem in the most powerful bounded-error model: the number-on-the-forehead model with k parties and arbitrary classical or quantum communication. We obtain a communication lower bound of Omega(√(n)/2k*k) bits, which is essentially optimal. Proving it was a longstanding open problem even in restricted settings, such as one-way classical protocols with k=4 parties (Wigderson 1997). The proof contributes a novel technique for lower bounds on multiparty communication, based on directional derivatives of communication protocols over the reals.