论文标题
学位限制强度分解和代数分支计划
Degree-restricted strength decompositions and algebraic branching programs
论文作者
论文摘要
我们分析了Kumar最近的二次代数分支程序大小下限方法（CCC 2017），用于功率和多项式。我们提供了这种方法的改进，在某些情况下可以更好地界限。 下边界依赖于由均质多项式定义的高表面上的Noether-Lefschetz型条件。在我们提供的明确示例中，下边界被证明是诉诸经典交叉点理论。 此外，我们使用类似的方法来改善多项式切片等级的已知下限方法。我们考虑了一系列多项式序列，这些序列曾经通过Shioda进行了研究，并表明对于这些多项式，改进的下限与已知的上限匹配。
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.
