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- Q17141967 subject Q7451559.
- Q17141967 abstract "Geometric complexity theory (GCT), is a research program in computational complexity theory proposed by Ketan Mulmuley. 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. 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 algebraic complexity classes. Proving that computing the permanent cannot be efficiently reduced to computing determinants is considered to be a major milestone for the program. These computational problems can be characterized by their symmetries. The program aims at utilizing these symmetries for proving lower bounds.The approach is considered by some to be the only viable currently active program to separate P from NP. However, Ketan Mulmuley believes the program, if viable, is likely to take about 100 years before it can settle the P vs. NP problem.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 relativization and natural proofs for proving general lower bounds.".
- Q17141967 wikiPageExternalLink 17629.
- Q17141967 wikiPageExternalLink gct.
- Q17141967 wikiPageExternalLink gct.cs.uchicago.edu.
- Q17141967 wikiPageExternalLink workshop_alggeometry1.html.
- Q17141967 wikiPageWikiLink Q1143357.
- Q17141967 wikiPageWikiLink Q1197709.
- Q17141967 wikiPageWikiLink Q13220368.
- Q17141967 wikiPageWikiLink Q178546.
- Q17141967 wikiPageWikiLink Q180969.
- Q17141967 wikiPageWikiLink Q205084.
- Q17141967 wikiPageWikiLink Q2431134.
- Q17141967 wikiPageWikiLink Q3495447.
- Q17141967 wikiPageWikiLink Q4791120.
- Q17141967 wikiPageWikiLink Q5157642.
- Q17141967 wikiPageWikiLink Q5535491.
- Q17141967 wikiPageWikiLink Q628036.
- Q17141967 wikiPageWikiLink Q6395317.
- Q17141967 wikiPageWikiLink Q6980761.
- Q17141967 wikiPageWikiLink Q7451559.
- Q17141967 wikiPageWikiLink Q746242.
- Q17141967 wikiPageWikiLink Q846354.
- Q17141967 comment "Geometric complexity theory (GCT), is a research program in computational complexity theory proposed by Ketan Mulmuley. 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. 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.".
- Q17141967 label "Geometric complexity theory".