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It has been shown that if P != NP, then GI is in that valley.

Could you point to a reference? Is this true even if P != NP, but NP = coNP?




This pdf (http://www.cs.princeton.edu/theory/complexity/ipchap.pdf) which is a draft chapter from a book by Arora and Barak, shows that if GI is NP-complete, then the polynomial hierarchy collapses to the second level. Collapse to the first level is when NP=coNP. So this is slightly weaker even than that.




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