Arithmetic Circuits and the Hadamard Product of Polynomials

Abstract

Motivated by the Hadamard product of matrices we define the Hadamard product of multivariate polynomials and study its arithmetic circuit and branching program complexity. We also give applications and connections to polynomial identity testing. Our main results are the following. • We show that noncommutative polynomial identity testing for algebraic branching programs over rationals is complete for the logspace counting class C=L, and over fields of characteristic p the problem is in ModpL/poly. • We show an exponential lower bound for expressing the Raz-Yehudayoff polynomial as the Hadamard product of two monotone multilinear polynomials. In contrast the Permanent can be expressed as the Hadamard product of two monotone multilinear formulas of quadratic size

Similar works

Full text

thumbnail-image
oai:CiteSeerX.psu:10.1.1.170.8833Last time updated on 10/22/2014

This paper was published in CiteSeerX.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.