布尔函数的偏微分编码
On Partial Differential Encodings of Boolean Functions
摘要：
我们介绍了布尔函数的偏微分编码作为衡量布尔函数复杂性的一种方法。这些编码使我们能够从群作用中导出用于指定布尔函数的偏微分编码的多项式的Chow秩的非平凡界。我们还介绍了偏微分编码的变种，称为偏微分程序。我们表明，这样的计划最佳描述重要的家庭多项式，包括行列式和永久。偏微分程序也可以定量地对比这两个多项式族。最后，我们从多项式结构的启发偏微分程序表现出无条件指数分离之间的高阶超图同构实例和他们的子同构对应。
英文摘要：
We introduce partial differential encodings of Boolean functions as a way of measuring the complexity of Boolean functions. These encodings enable us to derive from group actions non-trivial bounds on the Chow-Rank of polynomials used to specify partial differential encodings of Boolean functions. We also introduce variants of partial differential encodings called partial differential programs. We show that such programs optimally describe important families of polynomials including determinants and permanents. Partial differential programs also enables to quantitively contrast these two families of polynomials. Finally we derive from polynomial constructions inspired by partial differential programs which exhibit an unconditional exponential separation between high order hypergraph isomorhism instances and their sub-isomorphism counterparts.
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