Devising an efficient deterministic – or even a nondeterministic sub-exponential time – algorithm for testing polynomial identities is a fundamental problem in algebraic comp...
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 say that a polynomial f(x1, . . . , xn) is indecomposable if it cannot be written as a product of two polynomials that are defined over disjoint sets of variables. The polynom...