Computing the Additive Complexity of Algebraic Circuits with Root Extracting

In this paper we study the complexity of constructing a hitting set for VP, the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. ...

We show that, for every homogeneous polynomial of degree $d$, if it has determinantal complexity at most $s$, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most $O(d^{5}s)$. Moreover, we show that for most ...$\mathrm{}$$$

We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph H to n-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new algorithms for ...$\mathsf{}$$\mathsf{}\mathsf{}$$\mathsf{}$