由不可约序集给出的格的对偶
Dualization in Lattices Given by Ordered Sets of Irreducibles
摘要：
有限格上单调布尔函数的对偶可以通过将其最小值1的集合变换为最大值0的集合来表示。在本文中，我们考虑有限格由它们的交和并不可约（即，作为形式上下文的概念格）。我们表明，在这种情况下，二元论是相当于所谓的最小假设的枚举。在通常的对偶设置，其中一个格是由其元素的有序集，对偶在这种情况下，是不可能的输出多项式时间，除非P = NP。然而，如果格是分配的，对偶被证明是可能的亚指数时间。
英文摘要：
Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and join irreducibles (i.e., as a concept lattice of a formal context). We show that in this case dualization is equivalent to the enumeration of so-called minimal hypotheses. In contrast to usual dualization setting, where a lattice is given by the ordered set of its elements, dualization in this case is shown to be impossible in output polynomial time unless P = NP. However, if the lattice is distributive, dualization is shown to be possible in subexponential time.
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