The query complexity of program checking by constant-depth circuits

Abstract

We study program result checking using AC0 circuits as checkers. We focus on the number of queries made by the checker to the program being checked and we term this as the query complexity of the checker for the given problem. We study the query complexity of deterministic and randomized AC0 checkers for certain P-complete and NC1-complete problems. We show that for each ∈ > 0, Ω(n1-∈) is a lower bound to the query complexity of deterministic AC0 checkers for the considered problems, for inputs of length n. On the other hand, we show that suitably encoded complete problems for P and NC1 have randomized AC0 checkers of constant query complexity. The latter results are proved using techniques from the PCP(n3, 1) protocol for 3-SAT in [4].