Name
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 (Shpilka & Volkovich, 2010). |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s00037-015-0102-y | Computational Complexity |
Keywords | Field | DocType |
Arithmetic circuits, polynomial identity testing, polynomial factorization, 65Y04 | Discrete mathematics,Polynomial identity testing,Stable polynomial,Combinatorics,Polynomial matrix,Polynomial,Polynomial long division,Monic polynomial,Matrix polynomial,Mathematics,Factorization of polynomials | Journal |
Volume | Issue | ISSN |
24 | 2 | 1420-8954 |
Citations | PageRank | References |
5 | 0.45 | 18 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Swastik Kopparty | 1 | 384 | 32.89 |
| Shubhangi Saraf | 2 | 263 | 24.55 |
| Amir Shpilka | 3 | 1095 | 64.27 |