Suppose P = BPP.
Then we know there exist pseudorandom number generators vs P.
Suppose the adversary is NP.
Now, any pseudorandom number generator that only uses P will fail. (Since NP can invert one-way functions, and thus break any pseudorandom number generator based on them.)
How powerful do we have to allow the generator to be (EXP?) in order to generate a pseudorandom sequence that can fool NP?
[Context: reduced some open problem to this.]
[EDIT: Adversary does NOT have an NP oracle. Adversary is NP]