Testing low-degree polynomials over GF (2)

N Alon, T Kaufman, M Krivelevich, S Litsyn, D Ron

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


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(1ϵ+k4k)O(1ϵ+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(1ϵ+2k)Ω(1ϵ+2k) queries.
Original languageAmerican English
Title of host publication6th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2003 and 7th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2003
EditorsSanjeev Arora, Klaus Jansen, José D. P. Rolim, Amit Sahai
PublisherSpringer Berlin Heidelberg
StatePublished - 2003

Bibliographical note

Place of conference:USA


Dive into the research topics of 'Testing low-degree polynomials over GF (2)'. Together they form a unique fingerprint.

Cite this