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We develop a novel technique for communication lower bounds, the pattern matrix method. Specifically, fix an arbitrary function f : {0, 1}n → {0, 1} and let Af be the matrix whose columns are each an(More)
We introduce the notion of a halfspace matrix, which is a sign matrix A with rows indexed by linear threshold functions f, columns indexed by inputs x ∈ {− 1, 1} n , and the entries given by A f,x =(More)