Arithmetic Circuits and the Hadamard Product of Polynomials
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[$\bullet$] 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.
\end{itemize}
Hadamard product
identity testing
lower bounds
algebraic branching programs
25-36
Regular Paper
Vikraman
Arvind
Vikraman Arvind
Pushkar S.
Joglekar
Pushkar S. Joglekar
Srikanth
Srinivasan
Srikanth Srinivasan
10.4230/LIPIcs.FSTTCS.2009.2304
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
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