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It is known that $\textbf{AM}[O(1)] = \textbf{AM}$.

Since $\textbf{IP}=\textbf{PSPACE}$ we have $\textbf{AM}[poly(n)] = \textbf{PSPACE}$.

Can we say something about $\textbf{AM}[ f(n)]$, where $f$ is a function between $O(1)$ and $poly(n)$?

(For example, $f(n) = \log n$.)

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