Testing low-degree polynomials over GF(2)
| Venue: | RANDOM-APPROX 2003 |
| Citations: | 36 - 4 self |
BibTeX
@INPROCEEDINGS{Alon_testinglow-degree,
author = {Noga Alon and Tali Kaufman and Michael Krivelevich and Simon Litsyn and Dana Ron},
title = {Testing low-degree polynomials over GF(2)},
booktitle = { RANDOM-APPROX 2003},
year = {},
pages = {188--199},
publisher = {}
}
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Abstract
Abstract. We describe an efficient randomized algorithm to test if a given binary function � � ����� � � ���� � is a low-degree polynomial (that is, a sum of low-degree monomials). For a given integer � � � and a given real � � �, the algorithm queries � at � � � � � ��� � points. If � is a polynomial of degree at most �, the algorithm always accepts, and if the value of � has to be modified on at least an � fraction of all inputs in order to transform it to such a polynomial, then the algorithm rejects with probability at least ���. Our result is essentially tight: Any algorithm for testing degree- � polynomials over � � �� � must perform � � � � � �� � queries. 1
