## 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(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 language | American English |
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Title of host publication | 6th 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 |

Editors | Sanjeev Arora, Klaus Jansen, José D. P. Rolim, Amit Sahai |

Publisher | Springer Berlin Heidelberg |

State | Published - 2003 |