Factorization of Polynomials Given by Arithmetic Branching Programs

Abstract

Given a multivariate polynomial computed by an arithmetic branchingprogram (ABP) of size s, we show that all its factors can becomputed by arithmetic branching programs of size poly(s).Kaltofen gave a similar result for polynomials computed byarithmetic circuits. The previously known best upper bound forABP-factors was poly (s^{ {rm log} s}) .