Is it known that $\textbf{BPP} \subseteq \textbf{P}^{\textbf{NP}}$?

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    No, it’s not known. However, $\mathrm{BPP\subseteq MA\subseteq S_2P\subseteq ZPP^{NP}}$. – Emil Jeřábek Aug 8 at 11:31
  • Looks like an answer to me. – Auberon Aug 10 at 8:39

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