We study the problem, given a hypergraph $\mathcal{H}$, how to generate its transversal (or dual) hypergraph $\mathcal{G}$, using tools from Boolean resolution. We show how to compute the residual dual of $\mathcal{H}$ given a subset $\mathcal{E}$ of its minimal transversals. This is the hypergraph whose minimal transversals are exactly those missing from $\mathcal{E}$ to become the dual of $\mathcal{H}$. We give a novel algorithm for the problem based on the notion of subtransversal. Though its complexity is superpolynomial, it gives new insight to the problem of hypergraph duality. Another variant of the algorithm seems also promising to efficiently test hypergraph duality in practice.

中文翻译：

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横向超图生成问题的基于分辨率的算法

给定一个超图，我们研究这个问题 $\mathcal{H}$，如何生成其横向（或对偶）超图 $\mathcal{G}$，使用布尔解析工具。我们展示如何计算剩余双重的$\mathcal{H}$ 给定一个子集 $\mathcal{Ë}$最小的横向。这是超图，其最小横向恰好是那些$\mathcal{Ë}$ 成为 $\mathcal{H}$。我们基于子横向的概念提出了一种新颖的算法。尽管其复杂度是超多项式，但它为超图对偶问题提供了新的见解。该算法的另一个变体似乎也有望在实践中有效地测试超图对偶。