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

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

2007-12-27

arxiv.org/abs/0712.4279v2

Computer Science

Computational Complexity

23 pages. Added background to method and references to more recent work. Journal version to appear in Computational Complexity

Scientific paper

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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