Codd's rule of entity integrity stipulates that every table has a primary key. Hence, the attributes of the primary key carry unique and complete value combinations. In practice, data cannot always meet such requirements. Previous work proposed the superior notion of key sets for controlling entity integrity. We establish a linear-time algorithm for validating whether a given key set holds on a given data set, and demonstrate its efficiency on real-world data. We establish a binary axiomatization for the associated implication problem, and prove its coNP-completeness. However, the implication of unary by arbitrary key sets has better properties. The fragment enjoys a unary axiomatization and is decidable in quadratic time. Hence, we can minimize overheads before validating key sets. While perfect models do not always exist in general, we show how to compute them for any instance of our fragment. This provides computational support towards the acquisition of key sets.

中文翻译：

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使用键集控制实体完整性

Codd的实体完整性规则规定，每个表都有一个主键。因此，主键的属性带有唯一和完整的值组合。实际上，数据不能总是满足这些要求。先前的工作提出了用于控制实体完整性的密钥集的高级概念。我们建立了一个线性时间算法来验证给定的键集是否保存在给定的数据集上，并证明其在现实数据中的效率。我们为关联的蕴涵问题建立一个二进制公理化，并证明其coNP完整性。但是，任意键集对一进制的暗示具有更好的属性。该片段具有一元公理化，并且可以在二次时间内确定。因此，我们可以在验证密钥集之前最小化开销。尽管通常并不总是存在完美的模型，我们展示了如何为片段的任何实例计算它们。这为密钥集的获取提供了计算支持。