Name
Title | ||
|---|---|---|
Randomness Efficient Testing of Sparse Black Box Identities of Unbounded Degree over the Reals |
Abstract | ||
|---|---|---|
We construct a hitting set generator for sparse multivariate polynomials over the reals. The seed length of our generator is O(log(2)(mn/epsilon)) where m is the number of monomials, n is number of variables, and 1 - epsilon is the hitting probability. The generator can be evaluated in time polynomial in logm, n, and log 1/epsilon. This is the first hitting set generator whose seed length is independent of the degree of the polynomial. The seed length of the best generator so far by Klivans and Spielman [16] depends logarithmically on the degree. From this, we get a randomized algorithm for testing sparse black box polynomial identities over the reals using O(log(2)(mn/epsilon)) random bits with running time polynomial in log m, n, and log 1/epsilon. We also design a deterministic test with running time (O) over tilde (m(3)n(3)). Here, the (O) over tilde -notation suppresses polylogarithmic factors. The previously best deterministic test by Lipton and Vishnoi [18] has a running time that depends polynomially on log delta, where delta is the degree of the black box polynomial. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.4230/LIPIcs.STACS.2011.555 | Leibniz International Proceedings in Informatics |
Keywords | DocType | Volume |
Descartes' rule of signs,polynomial identity testing,sparse polynomials,black box testing | Conference | 9 |
ISSN | Citations | PageRank |
1868-8969 | 1 | 0.36 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Markus Bläser | 1 | 326 | 34.03 |
| Christian Engels | 2 | 10 | 3.95 |