## Circuit lower bounds for Merlin-Arthur classes (2007)

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Venue: | In Proc. ACM STOC |

Citations: | 11 - 1 self |

### BibTeX

@INPROCEEDINGS{Santhanam07circuitlower,

author = {Rahul Santhanam},

title = {Circuit lower bounds for Merlin-Arthur classes},

booktitle = {In Proc. ACM STOC},

year = {2007},

pages = {275--283},

publisher = {Manuscript}

}

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### Abstract

We show that for each k> 0, MA/1 (MA with 1 bit of advice) doesn’t have circuits of size nk. This implies the first superlinear circuit lower bounds for the promise versions of the classes MA, AM and ZPP NP We extend our main result in several ways. For each k, we give an explicit language in (MA ∩ coMA)/1 which doesn’t 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/nk fraction of inputs of length n by circuits of size nk. Furthermore, we prove that MA does not have arithmetic circuits of size nk for any k. As a corollary to our main result, we obtain that derandomization of MA with O(1) advice implies the existence of pseudo-random generators computable using O(1) bits of advice. 1