Geometric complexity theory: Difference between revisions

Revision as of 12:38, 14 May 2013

Revision as of 12:39, 14 May 2013

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The idea behind the approach is to adopt and develop advanced tools in [[algebraic geometry]] and [[representation 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 [[Permanant]] cannot be efficiently reduced to [[Determinant]] 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 serious program to separate [[P (complexity) | P]] from [[NP (complexity) | NP]]. However, according to Mulmuley the program is likely to take hundreds of 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 argument for the program avoiding all known [[barriers (complexity) | barriers]] for proving general lower-bounds.