It is well known that any proof resolving the P vs NP question must overcome relativization, natural proofs and algebrization barriers. The following diagram partitions the proof space into different regions. For example, $RN$ corresponds to the set of proofs that relativize and naturalize. $GCT$ (Geometric Complexity Theory) is of course the strictly outside region.Name some proofs along with the best known regions they belong to. Place them in a best possible way i.e., if a proof is known to relativize, naturalize and algebrize then it should be placed in $RNA$ not just in $RN$. If a proof relativizes but does not naturalize it belongs to $R$ ${\setminus}$ $N$ and so on.
Proofs, Barriers and P vs NP
cc.complexity theory;proofs;barriers;p vs np