Efficiently Testing Sparse GF(2) Polynomials

Ilias Diakonikolas, Homin K. Lee, Kevin Matulef, Rocco A. Servedio, Andrew Wan

Abstract: We give the first algorithm that is both query-efficient and time-efficient for testing whether an unknown function f: {0,1} n →{0,1} is an s-sparse GF(2) polynomial versus ε-far from every such polynomial. Our algorithm makes poly(s,1/ε) black-box queries to f and runs in time n ·poly(s,1/ε). The only previous algorithm for this testing problem [DLM + 07] used poly(s,1/ε) queries, but had running time exponential in s and super-polynomial in 1/ε.