格中蕴涵基的对偶性
Dualization in lattices given by implicational bases
摘要：
最近证明了在输出多项式时间内，由蕴涵基给出的格的对偶是不可能的，除非P=NP。在本文中，我们证明了即使当蕴涵基中的前提的大小至多为2时，这一结果也成立。利用超图对偶证明了只要蕴涵基具有有界独立宽度（定义为具有独立结论的蕴涵的最大集合的大小），问题就可以在输出准多项式时间内得到解决.共享这个属性的格包括由区间序的理想编码的分配格，当独立宽度和前提的大小都等于1时。
英文摘要：
It was recently proved that the dualization in lattices given by implicational bases is impossible in output-polynomial time unless P=NP. In this paper, we~show that this result holds even when the premises in the implicational base are of size at most two. Then we show using hypergraph dualization that the problem can be solved in output quasi-polynomial time whenever the implicational base has bounded independent-width, defined as the size of a maximum set of implications having independent conclusions. Lattices that share this property include distributive lattices coded by the ideals of an interval order, when both the independent-width and the size of the premises equal one.
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