论文标题
布尔功能的准随机影响
Quasi-Random Influences of Boolean Functions
论文作者
论文摘要
我们检查了布尔函数的准随机属性等效类别的层次结构。特别是，我们证明了许多属性之间的等效性，包括平衡影响，光谱差异，局部强规则，有色或加权图的同态枚举以及与布尔函数以及$ k $ th阶严格的严格雪崩标准相关的超图。我们进一步构建了准随机布尔函数的家族，这些函数表现出我们的等效定理的特性，并将层次结构的水平分开。
We examine a hierarchy of equivalence classes of quasi-random properties of Boolean Functions. In particular, we prove an equivalence between a number of properties including balanced influences, spectral discrepancy, local strong regularity, homomorphism enumerations of colored or weighted graphs and hypergraphs associated with Boolean functions as well as the $k$th-order strict avalanche criterion amongst others. We further construct families of quasi-random boolean functions which exhibit the properties of our equivalence theorem and separate the levels of our hierarchy.
