交换自动机网络
Commutative automata networks
摘要：
自动机网络是f：Q Z $\rightarrow$ Q Z形式的映射，其中Q是有限字母表，Z是实体的集合;它们推广了元胞自动机和布尔网络。更新调度规定每个实体何时根据其本地函数fi更新其状态：Q Z $\rightarrow$ Q。一个主要的问题是研究一个给定的自动机网络在不同的更新时间表下的行为。在本文中，我们研究了自动机网络，在许多不同的更新计划下是不变的。这就产生了两个定义，局部交换网络和全局交换网络。我们研究了交换性和更新函数的不同形式的局部性之间的关系;一个主要结论是全局交换网络具有很强的动力学性质，而局部交换网络的约束要少得多。我们还给出了所有全局交换布尔网络的一个完整分类。
英文摘要：
Automata networks are mappings of the form f : Q Z $\rightarrow$ Q Z , where Q is a finite alphabet and Z is a set of entities; they generalise Cellular Automata and Boolean networks. An update schedule dictates when each entity updates its state according to its local function fi : Q Z $\rightarrow$ Q. One major question is to study the behaviour of a given automata networks under different update schedules. In this paper, we study automata networks that are invariant under many different update schedules. This gives rise to two definitions, locally commutative and globally commu-tative networks. We investigate the relation between commutativity and different forms of locality of update functions; one main conclusion is that globally commutative networks have strong dynamical properties, while locally commutative networks are much less constrained. We also give a complete classification of all globally commutative Boolean networks.
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。
