Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > DETAIL:

Revision(s):

Revision #1 to TR19-140 | 19th February 2020 15:14

Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings.

RSS-Feed




Revision #1
Authors: Ankit Garg, Christian Ikenmeyer, Visu Makam, Rafael Mendes de Oliveira, Michael Walter, Avi Wigderson
Accepted on: 19th February 2020 15:14
Downloads: 26
Keywords: 


Abstract:

We consider the problem of computing succinct encodings of lists of generators for invariant rings for group actions. Mulmuley conjectured that there are always polynomial sized such encodings for invariant rings of $\SL_n(\C)$-representations. We provide simple examples that disprove this conjecture (under standard complexity assumptions).

We develop a general framework, denoted \emph{algebraic circuit search problems}, that captures many important problems in algebraic complexity and computational invariant theory.
This framework encompasses various proof systems in proof complexity and some of the central problems in invariant theory as exposed by the Geometric Complexity Theory (GCT) program, including the aforementioned problem of computing succinct encodings for generators for invariant rings.



Changes to previous version:

Merging papers with the result of Michael and Christian for SL(n) actions


Paper:

TR19-140 | 7th October 2019 16:41

Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings.


Abstract:

We consider the problem of outputting succinct encodings of lists of generators for invariant rings. Mulmuley conjectured that there are always polynomial sized such encodings for all invariant rings. We provide simple examples that disprove this conjecture (under standard complexity assumptions).



ISSN 1433-8092 | Imprint