AI 中文总结
该研究证明0/1多面体顶点近似计数问题是NP困难的，无FPRAS除非RP=NP，通过图同态近似计数归约得到，思路来自GPT-5.6 Sol Ultra。
AI 中文摘要
我们证明，对于由有理线性不等式组表示的有界0/1多面体，其顶点的近似计数问题，粗略地说，是NP困难的。具体而言，除非RP=NP，否则该问题不存在完全多项式随机近似方案（FPRAS）。证明通过从给定图到特定四顶点图的同态近似计数问题归约得到，主要证明思路由GPT-5.6 Sol Ultra得出。
英文摘要
We show that approximately counting the vertices of a bounded 0/1 polytope, presented as a system of rational linear inequalities, is, informally speaking, NP-hard. In particular, there is no FPRAS for this problem unless RP=NP. The proof is by a reduction from approximately counting homomorphisms from a given graph to a particular four-vertex graph. The main proof ideas were found using GPT-5.6 Sol Ultra.
