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If we find a problem we know for sure is in NP but not in NP-complete or P, we'll have proved P!=NP. One approach then is to identify problems in NP (but not P) we haven't been able to show to be NP-complete so far and try to prove they aren't in that set. Any examples of such problems? Preferably one problem per answer?

Rohit Pandey
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  • https://cs.stackexchange.com/q/19543/755, https://cstheory.stackexchange.com/q/20930/5038 – D.W. Oct 02 '22 at 23:57

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The language constructed in the proof of Ladner's Theorem.

See also the Wikipedia page on the NP-intermediate class, which contains a list of problems that might be in NP-intermediate.

Steven
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