Circuit lower bounds for average-case MA

Abstract

Santhanam (2007) proved that MA/1 does not have circuits of size nk. We translate his result to the average-case setting by proving that there is a constant a such that for any k, there is a language in AvgMA that cannot be solved by circuits of size nk on more than the (Formula Presented.) fraction of inputs. In order to get rid of the non-uniform advice, we supply the inputs with the probability threshold that we use to determine the acceptance. This technique was used by Pervyshev (2007) for proving a time hierarchy for heuristic computations.