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...
In this paper we give reconstruction algorithms for depth-3 arithmetic circuits with k multiplication gates (also known as ΣΠΣ(k) circuits), where k = O(1). Namely, we give an ...
We demonstrate that the unbounded fan-out gate is very powerful. Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denot...
We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multiline...