We develop a new technique of proving lower bounds for the randomized communication complexity of boolean functions in the multiparty `Number on the Forehead' model. Our meth...
We study the circuit complexity of the powering function, defined as POWm(Z) = Zm for an n-bit integer input Z and an integer exponent m poly(n). Let LTd denote the class of func...
We study the complexity of locally list-decoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that co...
Much work has been done on learning various classes of "simple" monotone functions under the uniform distribution. In this paper we give the first unconditional lower bo...
Algorithmic tools for graphs of small treewidth are used to address questions in complexity theory. For both arithmetic and Boolean circuits, it is shown that any circuit of size ...