Degree-restricted strength decompositions and algebraic branching programs

Purnata Ghosal, Fulvio Gesmundo, Christian Ikenmeyer, Vladimir Lysikov
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引用次数: 2

Abstract

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.
受限度强度分解与代数分支规划
我们分析了库马尔最近提出的幂和多项式的二次代数分支程序大小下界证明方法(CCC 2017)。我们对该方法进行了改进,在某些情况下给出了更好的边界。下界依赖于由齐次多项式定义的超曲面上的Noether-Lefschetz型条件。在我们提供的显式例子中,利用经典的交点理论证明了下界。此外,我们使用类似的方法来改进已知的多项式切片秩下界方法。我们考虑了Shioda之前研究过的一个多项式序列,并证明了这些多项式的改进下界与已知上界相匹配。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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