{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:26:34Z","timestamp":1787340394832,"version":"build-2736575974"},"reference-count":50,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2009,1]]},"abstract":"<jats:p>We show that for each $k&gt;0$, $\\mathsf{MA}\/1$ ($\\mathsf{MA}$ 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 $\\mathsf{MA}$, $\\mathsf{AM}$, and $\\mathsf{ZPP}_{\\parallel}^{\\mathsf{NP}}$. We extend our main result in several ways. For each k, we give an explicit language in $(\\mathsf{MA}\\cap\\mathsf{coMA})\/1$ 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 $\\mathsf{MA}\/1$ 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 $\\mathsf{MA}$ does not have arithmetic circuits of size $n^k$ for any k. As a corollary to our main result, we obtain that derandomization of $\\mathsf{MA}\/O(1)$ implies the existence of pseudorandom generators computable using $O(1)$ bits of advice.<\/jats:p>","DOI":"10.1137\/070702680","type":"journal-article","created":{"date-parts":[[2009,9,2]],"date-time":"2009-09-02T18:07:04Z","timestamp":1251914824000},"page":"1038-1061","source":"Crossref","is-referenced-by-count":30,"title":["Circuit Lower Bounds for Merlin\u2013Arthur Classes"],"prefix":"10.1137","volume":"39","author":[{"given":"Rahul","family":"Santhanam","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,9,2]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"S. 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