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 SLn(C)-representations. We provide simple examples that disprove this conjecture (under standard complexity assumptions). We develop a general framework, denoted 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.
| Original language | English |
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| Title of host publication | 35th Computational Complexity Conference, CCC 2020 |
| Editors | Shubhangi Saraf |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959771566 |
| DOIs | |
| State | Published - 1 Jul 2020 |
| Externally published | Yes |
| Event | 35th Computational Complexity Conference, CCC 2020 - Virtual, Online, Germany Duration: 28 Jul 2020 → 31 Jul 2020 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
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| Volume | 169 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 35th Computational Complexity Conference, CCC 2020 |
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| Country/Territory | Germany |
| City | Virtual, Online |
| Period | 28/07/20 → 31/07/20 |
Bibliographical note
Publisher Copyright:© Ankit Garg, Christian Ikenmeyer, Visu Makam, Rafael Oliveira, Michael Walter, and Avi Wigderson; licensed under Creative Commons License CC-BY 35th Computational Complexity Conference (CCC 2020).
Keywords
- Generators for invariant rings
- Succinct encodings