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Questions about the hardest problems in NP, i.e. of those that can be solved in polynomial time by nondeterministic Turing machines.
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Is an oracle ever useful if you can't control the input instances?
Let's say $F$ is an oracle for a problem in $\mathbb{NP}$, but I cannot call this oracle with any input instance. Instead, whenever I call $F$ I get returned a random instance and solution. Thus, I …