Disjointness is hard in the multiparty number-on-the-forehead model

Abstract

We show that disjointness requires randomized communication Ω({n 1/(k+1)/22k) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound for k ≥ 3 was logn/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 Lovász-Schrijver proofs. © 2009 Birkhäuser Verlag, Basel.