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

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

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

<p>(For example, $f(n) = \log n$.)</p>

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2017-02-17T09:48:09.810Z
@RickyDemer Careful, you are next to a caged animal.
Emil Jeřábek
<cc.complexity-theory><complexity-classes><interactive-proofs>
What can we say about AM[log n]?
Alexey Milovanov
# What can we say about AM[log n]?

(Asked by: username_0 on 2017-02-16)

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

**Tags:** cc.complexity-theory, complexity-classes, interactive-proofs

> **Comments:**
> **username_1**: @RickyDemer Careful, you are next to a caged animal.  

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