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- Geometric_complexity_theory 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 often considered 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.".
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- Geometric_complexity_theory wikiPageExternalLink gct.
- Geometric_complexity_theory wikiPageExternalLink gct.cs.uchicago.edu.
- Geometric_complexity_theory wikiPageExternalLink workshop_alggeometry1.html.
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- Geometric_complexity_theory wikiPageRevisionID "672299994".
- Geometric_complexity_theory wikiPageWikiLink Algebraic_geometry.
- Geometric_complexity_theory wikiPageWikiLink Arithmetic_circuit_complexity.
- Geometric_complexity_theory wikiPageWikiLink Category:Computational_complexity_theory.
- Geometric_complexity_theory wikiPageWikiLink Computational_complexity_theory.
- Geometric_complexity_theory wikiPageWikiLink Computing_the_permanent.
- Geometric_complexity_theory wikiPageWikiLink Cstheory.
- Geometric_complexity_theory wikiPageWikiLink Determinant.
- Geometric_complexity_theory wikiPageWikiLink Geometric_invariant_theory.
- Geometric_complexity_theory wikiPageWikiLink Ketan_Mulmuley.
- Geometric_complexity_theory wikiPageWikiLink NP_(complexity).
- Geometric_complexity_theory wikiPageWikiLink Natural_proof.
- Geometric_complexity_theory wikiPageWikiLink Oracle_machine.
- Geometric_complexity_theory wikiPageWikiLink P_(complexity).
- Geometric_complexity_theory wikiPageWikiLink P_versus_NP_problem.
- Geometric_complexity_theory wikiPageWikiLink P_vs._NP.
- Geometric_complexity_theory wikiPageWikiLink Reduction_(complexity).
- Geometric_complexity_theory wikiPageWikiLink Representation_theory.
- Geometric_complexity_theory wikiPageWikiLink Stack_Exchange.
- Geometric_complexity_theory wikiPageWikiLink Symmetry_(mathematics).
- Geometric_complexity_theory wikiPageWikiLink Symmetry_in_mathematics.
- Geometric_complexity_theory wikiPageWikiLinkText "Geometric complexity theory".
- Geometric_complexity_theory wikiPageWikiLinkText "geometric complexity theory".
- Geometric_complexity_theory hasPhotoCollection Geometric_complexity_theory.
- Geometric_complexity_theory wikiPageUsesTemplate Template:Reflist.
- Geometric_complexity_theory subject Category:Computational_complexity_theory.
- Geometric_complexity_theory hypernym Program.
- Geometric_complexity_theory type Work.
- Geometric_complexity_theory 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.".
- Geometric_complexity_theory label "Geometric complexity theory".
- Geometric_complexity_theory sameAs m.0vpxktz.
- Geometric_complexity_theory sameAs Q17141967.
- Geometric_complexity_theory sameAs Q17141967.
- Geometric_complexity_theory wasDerivedFrom Geometric_complexity_theory?oldid=672299994.
- Geometric_complexity_theory isPrimaryTopicOf Geometric_complexity_theory.