Prospects for Geometric Complexity Theory

2012 ◽  
Author(s):  
Peter Burgisser
Keyword(s):  
Complexity Theory ◽  
Geometric Complexity ◽  
Geometric Complexity Theory

scholarly journals No occurrence obstructions in geometric complexity theory

2018 ◽  
Vol 32 (1) ◽  
pp. 163-193 ◽  
Author(s):  
Peter Bürgisser ◽  
Christian Ikenmeyer ◽  
Greta Panova
Keyword(s):  
Complexity Theory ◽  
Geometric Complexity ◽  
Geometric Complexity Theory

Guest Column

2021 ◽  
Vol 52 (4) ◽  
pp. 56-73
Author(s):  
Ben Volk
Keyword(s):  
Recent Work ◽  
Complexity Theory ◽  
Lower Bounds ◽  
Open Problem ◽  
Computational Models ◽  
Boolean Circuit ◽  
Geometric Complexity ◽  
Algebraic Version ◽  
Circuit Lower Bounds ◽  
Geometric Complexity Theory

Algebraic Natural Proofs is a recent framework which formalizes the type of reasoning used for proving most lower bounds on algebraic computational models. This concept is similar to and inspired by the famous natural proofs notion of Razborov and Rudich [RR97] for boolean circuit lower bounds, but, unlike in the boolean case, it is an open problem whether this constitutes a barrier for proving super-polynomial lower bounds for strong models of algebraic computation. From an algebraic-geometric viewpoint, it is also related to basic questions in Geometric Complexity Theory (GCT), and from a meta-complexity theoretic viewpoint, it can be seen as an algebraic version of the MCSP problem. We survey the recent work around this concept which provides some evidence both for and against the existence of an algebraic natural proofs barrier, with an emphasis on the di erent viewpoints and the connections to other areas.

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