关于一般网络上社会平衡的动力学（及对XOR-SAT的应用）
On the dynamics of Social Balance on general networks (with an application to XOR-SAT)
摘要：
我们研究离散动力系统的非确定性和概率版本（由于T。Antal，P. L. Krapivsky和S. Redner）的社会平衡理论的启发。我们研究了几类图的收敛时间的动态。我们的贡献包括：1.我们指出了三重动力学和广义的零化走超图之间的连接。特别是，这种连接使我们能够完全表征图中的递归状态，其中每条边最多属于两个三角形。2.我们还解决了超图不包含由一个或两个顶点组成的边的情况。3.我们证明了在所谓的“三元圈”图上，收敛时间是线性的。4.我们得到了2-正则三元单形G的收敛时间的三次上界。这个界可以进一步改进到一个依赖于G的Cheeger常数的量。特别是这提供了一些严格的对应以前的实验观察。我们还指出了一个应用程序的随机游走算法的分析在某些情况下的3-异或-SAT问题。
英文摘要：
We study nondeterministic and probabilistic versions of a discrete dynamical system (due to T. Antal, P. L. Krapivsky, and S. Redner) inspired by Heider's social balance theory. We investigate the convergence time of this dynamics on several classes of graphs. Our contributions include: 1. We point out the connection between the triad dynamics and a generalization of annihilating walks to hypergraphs. In particular, this connection allows us to completely characterize the recurrent states in graphs where each edge belongs to at most two triangles. 2. We also solve the case of hypergraphs that do not contain edges consisting of one or two vertices. 3. We show that on the so-called "triadic cycle" graph, the convergence time is linear. 4. We obtain a cubic upper bound on the convergence time on 2-regular triadic simplexes G. This bound can be further improved to a quantity that depends on the Cheeger constant of G. In particular this provides some rigorous counterparts to previous experimental observations. We also point out an application to the analysis of the random walk algorithm on certain instances of the 3-XOR-SAT problem.
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。
