摘要：In a sequence of fundamental results in the 1980s, Kaltofen (SICOMP 1985,
STOC’86, STOC’87, RANDOM’89) showed that factors of multivariate polynomials with
small arithmetic circuits have small arithmetic circuits. In other words, the complexity class
VP is closed under taking factors. A natural question in this context is to understand if
other natural classes of multivariate polynomials, for instance, arithmetic formulas, algebraic
branching programs, bounded-depth arithmetic circuits or the class VNP, are closed under
taking factors.
