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I changed the sentence saying that this program is "often considered to be the only viable approach" to say that it is "considered by some to be ...". I am an active researcher in the field, and I don't think this opinion is very popular. |
Milind Sohoni and Ketan Mulmuley together proposed GCT. I added Milind's name to the page. Tags: Mobile edit Mobile web edit |
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'''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 – [[P versus NP problem|whether P = NP]] – by showing that the complexity class [[P (complexity) | P]] is not equal to the complexity class [[NP (complexity) | NP]].
The idea behind the approach is to adopt and develop advanced tools in [[algebraic geometry]] and [[representation theory]] (i.e., [[geometric invariant theory]]) to prove lower bounds for problems. Currently the main focus of the program is on [[Arithmetic circuit complexity#Algebraic P and NP | algebraic complexity]] classes. Proving that [[computing the permanent]] cannot be efficiently [[Reduction (complexity)|reduced]] to computing [[determinant]]s is considered to be a major milestone for the program. These computational problems can be characterized by their [[symmetry (mathematics) | symmetries]]. The program aims at utilizing these symmetries for proving lower bounds.
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The program is pursued by several researchers in mathematics and theoretical computer science. Part of the reason for the interest in the program is the existence of arguments for the program avoiding known barriers such as [[Oracle machine|relativization]] and [[natural proof]]s for proving general lower bounds.
==References==
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