Degree-Restricted Strength Decompositions and Algebraic Branching Programs
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We analyze Kumar's recent quadratic algebraic branching program size lower bound proof method (CCC 2017) for the power sum polynomial. We present a refinement of this method that gives better bounds in some cases. The lower bound relies on Noether-Lefschetz type conditions on the hypersurface defined by the homogeneous polynomial. In the explicit example that we provide, the lower bound is proved resorting to classical intersection theory. Furthermore, we use similar methods to improve the known lower bound methods for slice rank of polynomials. We consider a sequence of polynomials that have been studied before by Shioda and show that for these polynomials the improved lower bound matches the known upper bound.
Original language | English |
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Title of host publication | 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2022 |
Editors | Anuj Dawar, Venkatesan Guruswami |
Number of pages | 15 |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
Publication date | 2022 |
Article number | 20 |
ISBN (Electronic) | 9783959772617 |
DOIs | |
Publication status | Published - 2022 |
Event | 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2022 - Chennai, India Duration: 18 Dec 2022 → 20 Dec 2022 |
Conference
Conference | 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2022 |
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Land | India |
By | Chennai |
Periode | 18/12/2022 → 20/12/2022 |
Series | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 250 |
ISSN | 1868-8969 |
Bibliographical note
Publisher Copyright:
© Fulvio Gesmundo, Purnata Ghosal, Christian Ikenmeyer, and Vladimir Lysikov; licensed under Creative Commons License CC-BY 4.0.
- Algebraic branching programs, Lower bounds, Slice rank, Strength of polynomials
Research areas
ID: 331252328