2026-07-22T10:50:44Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17412 2024-03-06T10:59:41Z ddc:004 open_access

Degree-Restricted Strength Decompositions and Algebraic Branching Programs Gesmundo, Fulvio Ghosal, Purnata Ikenmeyer, Christian Lysikov, Vladimir Lower bounds Slice rank Strength of polynomials Algebraic branching programs 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Fulvio Gesmundo and Purnata Ghosal and Christian Ikenmeyer and Vladimir Lysikov 2022 Is Part Of LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2022.20 urn:nbn:de:0030-drops-174127 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.20 eng https://creativecommons.org/licenses/by/4.0/legalcode