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Can you help me understand the class of problems solvable by a nondetermimistic Turing machine with an oracle for SAT running in polynomial time?

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Surely this class, being $\text{NP}^\text{NP}$, is by definition equal to $\Sigma_2^p$. In particular, if the Polynomial Hierarchy (PH) does not collapse, then it does not contain $\Pi_2^p$.

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  • $\begingroup$ Yes you are obviously right, I actually got confused with another question I meant to ask instead about P^NP. $\endgroup$
    – Liron
    Oct 23, 2009 at 23:09
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Yes, NP^SAT = NP^NP, because SAT is complete for NP. I don't know what else can be said about this class (it's not in the complexity zoo). See the wikipedia oracle page for more details.

By the way, the above "computer" tag is not very relevant, it should rather be "complexity", or "complexity-theory".

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Isn't that class NP^NP?

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