@inbook{865cbd11052a4325b3f5c76193914389,

title = "Testing low-degree polynomials over GF(2)",

abstract = "We describe an efficient randomized algorithm to test if a given binary function f : {0, 1}n → {0, 1} is a low-degree polynomial (that is, a sum of low-degree monomials). For a given integer k ≥ 1 and a given real ε > 0, the algorithm queries f at O(1/ε + k4k) points. If f is a polynomial of degree at most k, the algorithm always accepts, and if the value of f has to be modified on at least an ε fraction of all inputs in order to transform it to such a polynomial, then the algorithm rejects with probability at least 2/3. Our result is essentially tight: Any algorithm for testing degree-k polynomials over GF(2) must perform Ω(1/e + 2k) queries.",

author = "Noga Alon and Tali Kaufman and Michael Krivelevich and Simon Litsyn and Dana Ron",

note = "Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2003",

doi = "10.1007/978-3-540-45198-3_17",

language = "English (US)",

isbn = "3540407707",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "188--199",

editor = "Sanjeev Asora and Amit Sahai and Klaus Jansen and Rolim, {Jose D.P.}",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

address = "Germany",

}