Arithmetic Circuits and the Hadamard Product of Polynomials

Autor:	Arvind, V., Joglekar, Pushkar S., Srinivasan, Srikanth
Rok vydání:	2009
Předmět:	Computer Science - Computational Complexity
Druh dokumentu:	Working Paper
Popis:	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. 1. 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 $\ModpL/\Poly$. 2.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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0907.4006 Zobrazit plný text záznamu View this record from Arxiv