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Sep
2
comment Oracles and relativization in non-TM settings
Going back to the $P?NP$ setting, I don't really have a good understanding of what an $NP^A$-complete problem might look like. Or even if that concept makes sense. For an arbitrary oracle A, is there a nice type of problem such that all problems in $NP^A$ are polynomial-time reducible to a problem of that type?
Sep
2
comment Oracles and relativization in non-TM settings
Okay, thank you! That's very helpful. And I'm not looking at $P?NP$ in a graph theory context necessarily, the second part of my question is if there is some natural way to define a relativized version of a graph theory question -- I didn't think my example was particularly natural.
Sep
1
comment Is SAT in P^{SAT}?
Thank you. So the definition in Wikipedia is flat-out wrong? I have a followup question (related to the non-TM setting version of oracles), but I'll make that separate.