# Has Oracles actually provided intuition for proving anything in Complexity Theory?

[EDIT: I realize this question is soft. I realize some people want to close this question. The goal here is trying to answer the following question:

So I see these research papers that provide papers for oracles B s.t. C^B != D^B.

Question: How do I build on these results? [Besides proving other oracles?] Are there examples where people have techniques that utilize oracle separations? ]

Known:

For many classes C, D we do not know about C vs D, but we have oracles relative to which C^A = D^A, C^B != D^B.

Question:

Is there any class separation result that has been inspired by Oracles? I.e. the argument is that finding such oracles shows that these classes are "hard to separate", -- but does having examples of separating oracles actually help separate the class?

Is there any case where the existence of a B s.t. C^B != D^B somehow guided the proof of C != D ?

Thanks!

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If you think the question is soft, you should probably add the soft-question tag. –  Thierry Zell Sep 27 '11 at 17:56

IIRC, the circuit complexity classes like $\mathsf{AC^0}$ were studied originally for proving relativization results. A classical example is Furst, Saxe, and Sipser, "Parity, Circuits, and the Polynomial-Time Hierarchy".