Abstract. An algebraic branching program (ABP) is a directed acyclic graph, with a start vertex s, and end vertex t and each edge having a weight which is ...

Nov 26, 2019 · Abstract page for arXiv paper 1911.11793: A Quadratic Lower Bound for Algebraic Branching Programs and Formulas.

Jun 8, 2019 · In this paper, we show that any homogeneous algebraic branching program which computes the polynomial x 1 n + x 2 n + ⋯ + x n n has at least Ω ...

Any homogeneous ABP which computes the polynomial has at least vertices. Ω(nd). Page 26. Homogeneous ABP lower bounds. 26.

Let B be a homogeneous algebraic branching program over the field 1 which computes the polynomial P(n,d)(x). Then, the number of vertices in B is at least o(nd) ...

In general, an ABP computing an n-variate homogeneous polynomial of degree poly(n) can be homogenized with a polynomial blow-up in size. This is proved in a ...

Aug 1, 2017 · An ABP computes a polynomial in a natural way, as the sum of weights of all paths from s to t, where the weight of a path is the product of the ...

Jun 8, 2019 · Abstract. An algebraic branching program (ABP) is a directed acyclic graph, with a start vertex s, and end vertex t and each edge having a.

An ABP is said to be homogeneous if the polynomial computed at every vertex is homogeneous. In this paper, we show that any homogeneous algebraic branching ...

has at least o(n2) vertices. This improves upon the lower bound of o(n log n), which fol- lows from the classical result of Baur and Strassen [Str73a, ...