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They are some of the very few NP problems not known to be in P or to be NP-complete. The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate.
Geometric complexity theory (GCT), is a research program in computational complexity theory proposed by Ketan Mulmuley and Milind Sohoni. The goal of the program is to answer the most famous open problem in computer science – whether P = NP – by showing that the complexity class P is not equal to the complexity class NP.
In computational complexity theory, a natural proof is a certain kind of proof establishing that one complexity class differs from another one. While these proofs are in some sense "natural", it can be shown (assuming a widely believed conjecture on the existence of pseudorandom functions) that no such proof can possibly be used to solve the P vs. NP problem.
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Let P 1 and P 2 be two problems in FNP, with associated verification algorithms A 1, A 2. A reduction P 1 and P 2 is defined as two efficiently-computable functions, f and g, such that [3] f maps inputs x to P 1 to inputs f(x) to P 2 ; g maps outputs y to P 2 to outputs g(y) to P 1 ; For all x and y: if A 2 (f(x),y) returns true, then A 1 (x, g ...
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