TY - CHAP

T1 - Testing low-degree polynomials over GF(2)

AU - Alon, Noga

AU - Kaufman, Tali

AU - Krivelevich, Michael

AU - Litsyn, Simon

AU - Ron, Dana

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=35248821354&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-45198-3_17

DO - 10.1007/978-3-540-45198-3_17

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AN - SCOPUS:35248821354

SN - 3540407707

SN - 9783540407706

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 188

EP - 199

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Asora, Sanjeev

A2 - Sahai, Amit

A2 - Jansen, Klaus

A2 - Rolim, Jose D.P.

PB - Springer Verlag

ER -