样本依赖与连接依赖的等价性

以抽象代数为工具,探索了全样本依赖与全连接依赖之间的关系.首先,分别在全样本依赖集和全连接依赖集上建立等价关系,这两种等价关系都将作用相同的依赖视为等价依赖. 然后证明了在这两个等价关系下的商集分别构成么半群,并且这两个么半群是同构的.这就等于证明了全样本依赖类本质上等同于全连接依赖类.最后给出了一个关于全无环连接依赖的有趣结果.有关结果可以在关系数据库的设计中发挥积极作用.

Equivalence of the Template Dependencies and the Join Dependencies

The relationship between the total template dependencies and the total join dependencies is probed into by means of abstract algebra. First, two equ ivalence relations are defined in the set of the total template dependencies and the set of the total join dependencies respectively. The equivalence relations regard the dependencies that function is the same as equivalent dependencies. Th en, it is proved that two quotient sets under two equivalence relations constitute monoids respectively and there is an isomorphism mapping between the monoids, which shows that the class of the total join dependencies is essentially identical with the class of the total template dependencies. Finally, an interesting result about the total acyclic join dependencies is given. The relevant results will play active role in designing relational database schemes.