The Library
Homogeneous algebraic complexity theory and algebraic formulas
Tools
Dutta, Pranjal, Gesmundo, Fulvio, Ikenmeyer, Christian, Jindal, Gorav and Lysikov, Vladimir (2024) Homogeneous algebraic complexity theory and algebraic formulas. In: 15th Innovations in Theoretical Computer Science Conference (ITCS 2024), Berkeley, CA, USA, 30 Jan - 2 Feb 2024. Published in: Leibniz International Proceedings in Informatics (LIPIcs), 287 43:1-43:23. ISBN 9783959773096. doi:10.4230/LIPIcs.ITCS.2024.43 ISSN 1868-8969.
|
PDF
WRAP-homogeneous-algebraic-complexity-theory-algebraic-formulas-Ikenmeyer-2024.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (877Kb) | Preview |
Official URL: https://doi.org/10.4230/LIPIcs.ITCS.2024.43
Abstract
We study algebraic complexity classes and their complete polynomials under homogeneous linear projections, not just under the usual affine linear projections that were originally introduced by Valiant in 1979. These reductions are weaker yet more natural from a geometric complexity theory (GCT) standpoint, because the corresponding orbit closure formulations do not require the padding of polynomials. We give the first complete polynomials for VF, the class of sequences of polynomials that admit small algebraic formulas, under homogeneous linear projections: The sum of the entries of the non-commutative elementary symmetric polynomial in 3 by 3 matrices of homogeneous linear forms.
Even simpler variants of the elementary symmetric polynomial are hard for the topological closure of a large subclass of VF: the sum of the entries of the non-commutative elementary symmetric polynomial in 2 by 2 matrices of homogeneous linear forms, and homogeneous variants of the continuant polynomial (Bringmann, Ikenmeyer, Zuiddam, JACM '18). This requires a careful study of circuits with arity-3 product gates.
Item Type: | Conference Item (Paper) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
|||||||||||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | |||||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Computer science -- Mathematics, Geometry, Algebraic, Computational complexity, Polynomials | |||||||||||||||||||||
Journal or Publication Title: | Leibniz International Proceedings in Informatics (LIPIcs) | |||||||||||||||||||||
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik | |||||||||||||||||||||
ISBN: | 9783959773096 | |||||||||||||||||||||
ISSN: | 1868-8969 | |||||||||||||||||||||
Official Date: | 24 January 2024 | |||||||||||||||||||||
Dates: |
|
|||||||||||||||||||||
Volume: | 287 | |||||||||||||||||||||
Page Range: | 43:1-43:23 | |||||||||||||||||||||
DOI: | 10.4230/LIPIcs.ITCS.2024.43 | |||||||||||||||||||||
Status: | Peer Reviewed | |||||||||||||||||||||
Publication Status: | Published | |||||||||||||||||||||
Access rights to Published version: | Open Access (Creative Commons) | |||||||||||||||||||||
Date of first compliant deposit: | 21 February 2024 | |||||||||||||||||||||
Date of first compliant Open Access: | 21 February 2024 | |||||||||||||||||||||
RIOXX Funder/Project Grant: |
|
|||||||||||||||||||||
Conference Paper Type: | Paper | |||||||||||||||||||||
Title of Event: | 15th Innovations in Theoretical Computer Science Conference (ITCS 2024) | |||||||||||||||||||||
Type of Event: | Conference | |||||||||||||||||||||
Location of Event: | Berkeley, CA, USA | |||||||||||||||||||||
Date(s) of Event: | 30 Jan - 2 Feb 2024 | |||||||||||||||||||||
Related URLs: | ||||||||||||||||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year