Self-Testing/Correcting for Polynomials and for Approximate Functions

The study of self-testing/correcting programs was introduced in [8] in order to allow one to use program P to compute function f without trusting that P works correctly. A self-tester for f estimates the fraction of x for which P(x) = f(x); and a self-corrector for f takes a program that is correct on most inputs and turns it into a program that is correct on every input with high probability 1 . Both access P only as a black-box and in some precise way are not allowed to compute the function f. Self-correcting is usually easy when the function has the random self-reducibility property. One class of such functions that has this property is the class of multivariate polynomials over finite fields [4] [12]. We extend this result in two directions. First, we show that polynomials are random self-reducible over more general domains: specifically, over the rationals and over noncommutative rings. Second, we show that one can get self-correctors even when the program satisfies weaker co...

• Type: Conference
• Year: 1991
• Where: STOC
• Authors: Peter Gemmell, Richard J. Lipton, Ronitt Rubinfeld, Madhu Sudan, Avi Wigderson
• Keywords: Algorithms, Polynomial, Random Self-reducibility Property, Self-testing/correcting Programs, STOC 1991