二部有界度图上2-旋系统在树非唯一性区域内的#BIS-硬性
#BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region
摘要：
二部图上独立集的计数（#BIS）被认为是一个具有中等近似复杂度的规范计数问题.可以肯定的是，#BIS既没有FPRAS，也不像#SAT那样难以近似。我们在二分图上的两态自旋系统的一般框架下研究#BIS。我们定义了两个概念，近独立的相位相关自旋和一元对称性破缺。我们证明了在支持这两个概念的二分图上，任何2-自旋系统的配分函数都是BIS困难的。因此，我们分类的复杂性近似的反铁磁2-自旋系统的配分函数的有界度二部图。
英文摘要：
Counting independent sets on bipartite graphs (#BIS) is considered a canonical counting problem of intermediate approximation complexity. It is conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to approximate. We study #BIS in the general framework of two-state spin systems on bipartite graphs. We define two notions, nearly-independent phase-correlated spins and unary symmetry breaking. We prove that it is #BIS-hard to approximate the partition function of any 2-spin system on bipartite graphs supporting these two notions. As a consequence, we classify the complexity of approximating the partition function of antiferromagnetic 2-spin systems on bounded-degree bipartite graphs.
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。
