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Correcting a paraphrase of the referenced quotation: "Nevertheless, Mulmuley believes it will take about 100 years to carry out this program, if it works at all." |
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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.
The approach is often considered the only viable currently active program to separate [[P (complexity) | P]] from [[NP (complexity) | 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.<ref>{{citation
| last = Fortnow | first = Lance
| doi = 10.1145/1562164.1562186
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