We consider the problem of computing an $(s,d)$-hypernetwork in an acyclic F-hypergraph. This is a fundamental computational problem arising in directed hypergraphs, and is a foundational step in tackling problems of reachability and redundancy. This problem was previously explored in the context of general directed hypergraphs (containing cycles), where it is NP-hard, and acyclic B-hypergraphs, where a linear time algorithm can be achieved. In a surprising contrast, we find that for acyclic F-hypergraphs the problem is NP-hard, which also implies the problem is hard in BF-hypergraphs. This is a striking complexity boundary given that F-hypergraphs and B-hypergraphs would at first seem to be symmetrical to one another. We provide the proof of complexity and explain why there is a fundamental asymmetry between the two classes of directed hypergraphs.

我们考虑计算一个问题$（s,d）$-非循环F-超图中的超网络。这是有向超图中出现的一个基本计算问题，也是解决可达性和冗余问题的基础步骤。这个问题之前曾在一般有向超图（包含循环）和非循环 B 超图（可以实现线性时间算法）的上下文中进行过探讨，其中它是 NP 困难的。令人惊讶的是，我们发现对于无环 F 超图，该问题是 NP 困难的，这也意味着该问题在 BF 超图中是困难的。鉴于 F 超图和 B 超图乍一看似乎彼此对称，这是一个惊人的复杂性边界。我们提供了复杂性的证明，并解释了为什么两类有向超图之间存在基本的不对称性。