文章基本信息

标题：Closure Results for Polynomial Factorization
本地全文：下载
作者：Chi-Ning Chou ; Mrinal Kumar ; Noam Solomon 等
期刊名称：Theory of Computing
印刷版ISSN：1557-2862
电子版ISSN：1557-2862
出版年度：2019
卷号：15
页码：1-34
DOI：10.4086/toc.2019.v015a013
出版社：University of Chicago
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.
关键词：algebraic complexity; polynomial factorization circuit lower bounds; Polynomial; Identity Testing; Polynomial Identity Lemma