独特的按键喇叭功能
Unique key Horn functions
摘要：
给定一个关系数据库，键是一组属性，对这组属性的赋值唯一地确定了所有其他属性的值。数据库唯一地定义了一个纯Horn函数$h$，表示函数依赖关系。如果集合$A$中的属性值的知识确定属性$v$的值，则$A\rightarrow v$是$h$的隐式。如果$K$是数据库的键，则$K\rightarrow v$是$v$的所有属性的$h$的隐式。小尺寸的密钥在各种问题中起着至关重要的作用。我们提出的结构和复杂性的结果，纯霍恩函数的最小键集。我们刻画了存在唯一纯Horn函数的Sperner超图的特征，其中给定的超图为极小键集。此外，我们发现，识别这样的超图是co-NP-完全的，当每个超边的大小为2。在积极的一面，我们确定了几类图形的识别问题，可以决定在多项式时间。我们还提出了一个算法，生成一个纯霍恩函数的多项式延迟的最小密钥。通过建立键和目标集之间的连接，我们的方法可以用来生成所有的最小目标集的多项式延迟时，阈值由一个常数的限制。作为一个副产品，我们的证明表明，最小密钥问题至少是困难的最小目标集选择问题有界阈值。
英文摘要：
Given a relational database, a key is a set of attributes such that a value assignment to this set uniquely determines the values of all other attributes. The database uniquely defines a pure Horn function $h$, representing the functional dependencies. If the knowledge of the attribute values in set $A$ determines the value for attribute $v$, then $A\rightarrow v$ is an implicate of $h$. If $K$ is a key of the database, then $K\rightarrow v$ is an implicate of $h$ for all attributes $v$. Keys of small sizes play a crucial role in various problems. We present structural and complexity results on the set of minimal keys of pure Horn functions. We characterize Sperner hypergraphs for which there is a unique pure Horn function with the given hypergraph as the set of minimal keys. Furthermore, we show that recognizing such hypergraphs is co-NP-complete already when every hyperedge has size two. On the positive side, we identify several classes of graphs for which the recognition problem can be decided in polynomial time. We also present an algorithm that generates the minimal keys of a pure Horn function with polynomial delay. By establishing a connection between keys and target sets, our approach can be used to generate all minimal target sets with polynomial delay when the thresholds are bounded by a constant. As a byproduct, our proof shows that the Minimum Key problem is at least as hard as the Minimum Target Set Selection problem with bounded thresholds.
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