The Taub Faculty of Computer Science Events and Talks

We show that disjointness requires randomized communication Omega(n^{1/2k}/{(k-1)2^{k-1}2^{2^{k-1}}) in the general k-party number-on-the-forehead model of complexity. The previous best lower bound was Omega((log n)/k-1). By results of Beame, Pitassi, and Segerlind, this implies 2^{n^{Omega(1)} lower bounds on the size of tree-like Lovasz-Schrijver proof systems needed to refute certain unsatisfiable CNFs, and super-polynomial lower bounds on the size of any tree-like proof system whose terms are degree-d polynomial inequalities for d = loglog n -O(logloglog n).

Joint work with Troy Lee from Rutgers University