We show that proving exponential lower bounds on depth four arithmetic circuits imply exponential lower bounds for unrestricted depth arithmetic circuits. In other words, for expo...
We derive quadratic lower bounds on the ∗-complexity of sum-of-products-of-sums (ΣΠΣ) formulas for classes of polynomials f that have too few partial derivatives for the techn...
Abstract. We consider various extensions and modifications of Shannon's General Purpose Analog Computer, which is a model of computation by differential equations in continuou...
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...