论文标题
交换性自动机网络
Commutative automata networks
论文作者
论文摘要
自动机网络是f：q z $ \ rightarrow $ q z表格的映射，其中q是有限的字母，z是一组实体；它们概括了蜂窝自动机和布尔网络。更新时间表决定了每个实体根据其本地函数fi更新其状态何时：q z $ \ rightarrow $q。一个主要问题是在不同的更新时间表下研究给定自动机网络的行为。在本文中，我们研究了在许多不同的更新时间表下不变的自动机网络。这引起了两个定义，这些定义是本地交换和全球通讯性网络。我们研究了通勤性与更新功能的不同形式的局部性之间的关系；一个主要的结论是，全球交换性网络具有强大的动力学特性，而本地交换网络的受限范围要少得多。我们还提供了所有全球合理性布尔网络的完整分类。
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.
