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.

翻译：我们引入了部分差异编码布林函数,作为衡量布林函数复杂性的一种方法。 这些编码使我们能够从聚氨酯函数Chow-Rank上的非三边界限的团体行动中获取。 我们引入了部分差异编码的变体,称为部分差异程序。 我们显示,这种程序最恰当地描述包括决定因素和永久值在内的重要多元值家庭的重要家庭。 部分差异方案还能够对这两个多元值家庭进行定量对比。 最后,我们从部分差异方案所启发的多元值结构中获取,这些差异方案显示,高秩序高射量同系史实例及其次单系对等之间的无条件指数分化分化。