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How to prove if P = NP if problem Π ϵ NP-complete and Problem complement Πc ϵ NP? OR P = NP if NPC intersects with Co-NPC

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Proving $NP=co-NP$ doesn't necessarily mean that $P=NP$. Although, the other way around is correct: Assume $P=NP$, then $co-NP=co-P=P=NP$.

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You won't find anything useful with our current knowledge. However, a change to $\Pi^c\in \mbox{P}$ will get you $\mbox{P}=\mbox{NP}$.

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  • $\begingroup$ Maybe you could expand on this a bit? Won't find anything useful for what? $\endgroup$ – 6005 Jul 21 at 16:06

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