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» Elusive Functions and Lower Bounds for Arithmetic Circuits
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FOCS
2008
IEEE
14 years 1 months ago
Arithmetic Circuits: A Chasm at Depth Four
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...
Manindra Agrawal, V. Vinay
COCOON
2007
Springer
14 years 1 months ago
"Resistant" Polynomials and Stronger Lower Bounds for Depth-Three Arithmetical Formulas
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...
Maurice J. Jansen, Kenneth W. Regan
UMC
2000
13 years 11 months ago
Upper and Lower Bounds on Continuous-Time Computation
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...
Manuel Lameiras Campagnolo, Cristopher Moore
IPL
2007
111views more  IPL 2007»
13 years 7 months ago
Powering requires threshold depth 3
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...
Alexander A. Sherstov