@inproceedings{073d5e1c4ada40979f541290e7e9415c,

title = "Equivalence of polynomial identity testing and deterministic multivariate polynomial factorization",

abstract = "In this paper we show that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. Specifically, we show that given an arithmetic circuit (either explicitly or via black-box access) that computes a multivariate polynomial f, the task of computing arithmetic circuits for the factors of f can be solved deterministically, given a deterministic algorithm for the polynomial identity testing problem (we require either a white-box or a black-box algorithm, depending on the representation of f). Together with the easy observation that deterministic factoring implies a deterministic algorithm for polynomial identity testing, this establishes an equivalence between these two central derandomization problems of arithmetic complexity. Previously, such an equivalence was known only for multilinear circuits [SV10].",

keywords = "Polynomial identity testing, arithmetic circuits, factoring",

author = "Swastik Kopparty and Shubhangi Saraf and Amir Shpilka",

year = "2014",

doi = "https://doi.org/10.1109/CCC.2014.25",

language = "الإنجليزيّة",

isbn = "9781479936267",

series = "Proceedings of the Annual IEEE Conference on Computational Complexity",

publisher = "IEEE Computer Society",

pages = "169--180",

booktitle = "Proceedings - IEEE 29th Conference on Computational Complexity, CCC 2014",

address = "الولايات المتّحدة",

note = "29th Annual IEEE Conference on Computational Complexity, CCC 2014 ; Conference date: 11-06-2014 Through 13-06-2014",

}