关于计数反馈弧集的复杂性
On the complexity of counting feedback arc sets
摘要：
本文研究了有向图中反馈弧集计数问题的计算复杂性，突出了计数类的一些微妙而又常见的性质。统计基数$k$的反馈弧集个数和反馈弧集的总数是P-完全问题，而统计最小反馈弧集个数仅被证明是P-困难问题.实际上，后一个问题是#.OptP[log n]-完全的，因此如果它属于#P，那么P=NP。
英文摘要：
In this note we study the computational complexity of feedback arc set counting problems in directed graphs, highlighting some subtle yet common properties of counting classes. Counting the number of feedback arc sets of cardinality $k$ and the total number of feedback arc sets are #P-complete problems, while counting the number of minimum feedback arc sets is only proven to be #P-hard. Indeed, this latter problem is #.OptP[log n]-complete, hence if it belongs to #P then P=NP.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
