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 ,a ndZPP NP . We extend our main result in several ways. For each k ,w e give an explicit language in (MA ∩ coMA)/1 which does not have circuits of size nk. 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.

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