Disjointness is hard in the multi-party number on the forehead model

Troy Lee; Adi Shraibman

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arXiv · 0712.4279

Disjointness is hard in the multi-party number on the forehead model

Troy Lee·Adi Shraibman

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Abstract

We show that disjointness requires randomized communication Omega(n^{1/(k+1)}/2^{2^k}) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound for k >= 3 was log(n)/(k-1). Our results give a separation between nondeterministic and randomized multiparty number-on-the-forehead communication complexity for up to k=log log n - O(log log log n) many players. Also by a reduction of Beame, Pitassi, and Segerlind, these results imply subexponential lower bounds on the size of proofs needed to refute certain unsatisfiable CNFs in a broad class of proof systems, including tree-like Lovasz-Schrijver proofs.

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Troy Lee, Adi Shraibman. 2009-06-09. Disjointness is hard in the multi-party number on the forehead model. https://arxiv.org/abs/0712.4279

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