超图Horn函数
Hypergraph Horn functions
摘要：
Horn函数是布尔函数的一个子类，具有有趣的结构和计算性质。这些函数在代数、人工智能、组合学、计算机科学、数据库理论和逻辑学中起着基础性的作用。本文引入了超图Horn函数的子类，它推广了拟阵和等价关系。给出了超图Horn函数的蕴涵对偶和闭包算子的多重刻画，分别作为拟阵对偶和拟阵闭包的MacLane-Steinitz交换性质的推广.我们还研究了超图Horn函数的算法问题，并表明识别问题（即，决定给定的确定Horn CNF是否表示超图Horn函数）和关键实现（即，判定给定超图是否通过超图Horn函数实现为密钥集）可以在多项式时间内完成，而隐含集可以用多项式延迟生成。
英文摘要：
Horn functions form a subclass of Boolean functions possessing interesting structural and computational properties. These functions play a fundamental role in algebra, artificial intelligence, combinatorics, computer science, database theory, and logic. In the present paper, we introduce the subclass of hypergraph Horn functions that generalizes matroids and equivalence relations. We provide multiple characterizations of hypergraph Horn functions in terms of implicate-duality and the closure operator, which are respectively regarded as generalizations of matroid duality and Mac Lane-Steinitz exchange property of matroid closure. We also study algorithmic issues on hypergraph Horn functions, and show that the recognition problem (i.e., deciding if a given definite Horn CNF represents a hypergraph Horn function) and key realization (i.e., deciding if a given hypergraph is realized as a key set by a hypergraph Horn function) can be done in polynomial time, while implicate sets can be generated with polynomial delay.
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