Does the halting oracle separate P from NP?

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Newberry

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Aug 4, 2022, 10:15:32 AMAug 4
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Does the halting oracle separate P from NP?

B.H.

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Aug 4, 2022, 12:38:03 PMAug 4
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On Thursday, August 4, 2022 at 10:15:32 AM UTC-4, Newberry wrote:
> Does the halting oracle separate P from NP?

No, P^H = NP^H . In general, think of NP as a subset of EXP, which is a deterministic class that also has enough time to query the oracle for any language in H...both P and NP/EXP can run for at least one step to access the oracle for whatever problem in H. So ultimately, you get the same languages...P^H = NP^H = H.

-Philip White (philip...@yahoo.com)

Newberry

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Aug 5, 2022, 8:49:57 PMAug 5
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But halting is the hardest problem. So it should be harder than the
Solovay oracle, should it not?
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