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, $f(n) = \log n$.)
What can we say about AM[log n]?
cc.complexity theory;complexity classes;interactive proofs