Arithmetic Circuits and the Hadamard Product of Polynomials

Vikraman Arvind, Pushkar S. Joglekar & Srikanth Srinivasan
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. \begin{itemize} \item[$\bullet$] We show that noncommutative polynomial identity testing for algebraic branching programs over rationals is complete for the logspace counting class $\ceql$, and over fields of characteristic $p$ the problem is in $\ModpL/\Poly$. \item[$\bullet$]...