Learning polynomials with queries: The highly noisy case

Given a function f mappping n-variate inputs from a finite field F into F, we consider the task of reconstructing a list of all n-variate degree d polynomials which agree with f on a tiny but non-negligible fraction, /spl delta/, of the input space. We give a randomized algorithm for solving this task which accesses f as a black box and runs in time polynomial in 1//spl delta/, n and exponential in d, provided /spl delta/ is /spl Omega/(/spl radic/(d.