Improved low-degree testing and its applications

Abstract

A test proposed by Rubinfield and Sudan is studied where the strongest previously known connection states that a function passes the test with probability δ for some δ>7/8 if the function has agreement ≈δ with a polynomial of degree d. A strong analysis which shows that the preceding statement is true for δ≪0.5 is presented. The analysis uses a version of Hilbert irreducibility, a tool used in the factoring of multivariate polynomials. One of the consequences of this study was a self tester/corrector for any buggy program that (supposedly) computes a polynomial over a finite field.