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I am currently learning about NP and coNP related content and have been exposed to the$NP \overset{\text{?}}{=}coNP$ problem.

I would like to know what are the directions to work on if I want to prove that $NP=coNP$? For example, currently I know that if I can prove that a coNP-complete language belongs to NP, then I can prove that $NP=coNP$.

If I want to prove that $NP \neq coNP$, what are the directions to work in, or what results have already been obtained?

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There are no directions that are likely to be accessible to an amateur. The problem is believed to be extremely hard. No one knows of any directions that are believed to be very promising. Instead, I recommend that you work on a different problem.

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