Multi-linearity self-testing with relative error

Abstract

We investigate self-testing programs with relative error by allowing error terms proportional to the function to be computed. Until now, in numerical computation, error terms were assumed to be either constant or proportional to the p-th power of the magnitude of the input, for p ∈ [0; 1). We construct new self-testers with relative error for realvalued multi-linear functions defined over finite rational domains. The existence of such self-testers positively solves an open question in [KMS99]. Moreover, our self-testers are very efficient: they use few queries and simple operations.