Reconstruction of Generalized Depth-3 Arithmetic Circuits with Bounded Top Fan-in

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 algorithm that when given a black box holding a ΣΠΣ(k) circuit C over a field F as input, makes queries to the black box (possibly over a polynomial sized extension field of F) and outputs a circuit C computing the same polynomial as C. In particular we obtain the following results.

• Type: Conference
• Year: 2009
• Where: COCO
• Authors: Zohar Shay Karnin, Amir Shpilka
• Keywords: Black Box, COCO 2009, Depth-3 Arithmetic Circuits, Polynomial Sized Extension, Theoretical Computer Science