Equivalence of polynomial identity testing and deterministic multivariate polynomial factorization

Swastik Kopparty, Shubhangi Saraf, Amir Shpilka

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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].

Original languageEnglish
Title of host publicationProceedings - IEEE 29th Conference on Computational Complexity, CCC 2014
PublisherIEEE Computer Society
Pages169-180
Number of pages12
ISBN (Print)9781479936267
DOIs
StatePublished - 2014
Externally publishedYes
Event29th Annual IEEE Conference on Computational Complexity, CCC 2014 - Vancouver, BC, Canada
Duration: 11 Jun 201413 Jun 2014

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159

Conference

Conference29th Annual IEEE Conference on Computational Complexity, CCC 2014
Country/TerritoryCanada
CityVancouver, BC
Period11/06/1413/06/14

Keywords

  • Polynomial identity testing
  • arithmetic circuits
  • factoring

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