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This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.

5 votes

Characterize P^NP (a.k.a. Delta_2^p)

This class is also known as Δ2P. See the complexity zoo for more details and results.
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4 votes

How can one characterize NP^SAT?

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, …
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