Can NP-Intermediate exist if P = NP?

Posted by Jason Baker on Stack Overflow See other posts from Stack Overflow or by Jason Baker
Published on 2010-04-11T21:46:27Z Indexed on 2010/04/11 21:53 UTC
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complexity

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np-complete

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p

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np

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np-intermediate

My understanding is that Ladner's theorem is basically this:

P != NP implies that there exists a set NPI where NPI is not in P and NPI is not NP-complete

What happens to this theorem if we assume that P = NP rather than P != NP? We know that if NP Intermediate doesn't exist, then P = NP. But can NP Intermediate exist if P = NP?

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