CIRCUIT LOWER BOUNDS FOR MERLIN-ARTHUR CLASSES

We show that for each k > 0, MA/1 ( MA with 1 bit of advice) does not have circuits of size n(k). This implies the first superlinear circuit lower bounds for the promise versions of the classes MA, AM, and ZPP(parallel to)(NP). We extend our main result in several ways. For each k, we give an explicit language in (MA boolean AND coMA)/1 which does not have circuits of size n(k). We also adapt our lower bound to the average-case setting; i.e., we show that MA/1 cannot be solved on more than 1/2 + 1/n(k) fraction of inputs of length n by circuits of size n(k). Furthermore, we prove that MA does not have arithmetic circuits of size n(k) for any k. As a corollary to our main result, we obtain that derandomization of MA/O(1) implies the existence of pseudorandom generators computable using O(1) bits of advice.