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.

翻译：我们研究布尔函数准随机特性等等同等级的等级,特别是,我们证明若干特性之间的等同等级,包括均衡影响、光谱差异、地方强烈的规律性、与布尔函数有关的彩色或加权图表的同质性查点和高音,以及美元等级的严格雪崩标准等。我们进一步建造具有准兰布林函数的家庭,这些功能体现了我们等同理论的特性,并区分了我们的等级层次。