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Are there any references covering this?

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As well as implying NP=co-NP, it would also imply that BQP contained NP.

It would also seem to imply that hard instances of NP-complete problems were easy to generate.

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Since integer factorization is known to be in both NP and co-NP, a proof that it is NP-complete would imply NP = co-NP, which is considered highly unlikely.

There is an interesting discussion at this old post by Lance Fortnow.

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  • $\begingroup$ It would be weakly np-complete because a pseudo-polytime algorithim exists on a classical machine. Just loop through (integer 1, input-value). Where input-value is the x amount of steps. $\endgroup$ – Travis Wells Apr 29 at 15:37

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