论文标题
独立的封闭操作集
Independent sets of closure operations
论文作者
论文摘要
在本文中，引入了独立的封闭操作集。我们以独立集的方式表征了封闭操作的最小键和抗基键。我们建立了基于独立集的封闭操作的最小键和抗基键之间的连接的表达式。我们构建了两种组合算法，以根据独立集合找到给定闭合操作的所有最小键和所有距离。我们估计这些算法的时间复杂性。最后，我们给出了关于关闭操作的非键的NP完整问题。
In this paper independent sets of closure operations are introduced. We characterize minimal keys and antikeys of closure operations in terms of independent sets. We establish an expression on the connection between minimal keys and antikeys of closure operations based on independent sets. We construct two combinatorial algorithms for finding all minimal keys and all antikeys of a given closure operation based on independent sets. We estimate the time complexity of these algorithms. Finally, we give an NP-complete problem concerning nonkeys of closure operations.
