Hardness amplification in proof complexity
Proceedings of the forty-second ACM symposium on Theory of computing
ACM SIGACT News
Composition theorems in communication complexity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
The multiparty communication complexity of set disjointness
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Making polynomials robust to noise
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
The NOF multiparty communication complexity of composed functions
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Communication lower bounds using directional derivatives
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Hadamard tensors and lower bounds on multiparty communication complexity
Computational Complexity
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We prove an n^Omega(1)/4^k lower bound on the randomized k-party communication complexity of depth 4 AC^0 functions in the number-on-forehead (NOF) model for up to Theta(log n) players. These are the first non-trivial lower bounds for general NOF multiparty communication complexity for any AC^0 function for omega(log log n) players. For non-constant k the bounds are larger than all previous lower bounds for any AC^0 function even for simultaneous communication complexity. Our lower bounds imply the first super polynomial lower bounds for the simulation of AC^0 by MAJ-SYMM-AND circuits, showing that the well-known quasipolynomial simulations of AC^0 by such circuits are qualitatively optimal, even for formulas of small constant depth. We also exhibit a depth 5 formula in NPc-BPPc for up to Theta(log n) players and derive an Omega(2^{sqrt{log n}/sqrt{k}}) lower bound on the randomized k-party NOF communication complexity of set disjointness for up to Theta(log^{1/3} n) players which is significantly larger than the O(log log n) players allowed in the best previous lower bounds for multiparty set disjointness. We prove other strong results for depth 3 and 4 AC^0 functions.