An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. The global dynamics of the network is then induced by an update scheme describing which nodes are updated at each time step. We study how update schemes can compensate the limitations coming from symmetric local interactions. Our approach is based on intrinsic simulations and universality and we study both dynamical and computational complexity. By considering several families of concrete symmetric AN under several different update schemes, we explore the edge of universality in this two-dimensional landscape. On the way, we develop a proof technique based on an operation of glueing of networks, which allows to produce complex orbits in large networks from compatible pseudo-orbits in small networks.

中文翻译：

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对称与异步：自动机网络的普遍性边缘

自动机网络（AN）是一个有限图，其中每个节点都具有一个有限字母表示的状态，并配备有一个局部图，该图根据节点的邻居来定义该节点的状态演变。然后，通过描述每个时间步骤更新哪些节点的更新方案来引发网络的全局动态。我们研究更新方案如何补偿对称本地交互产生的限制。我们的方法基于内在的模拟和通用性，我们研究动态和计算复杂性。通过在几种不同的更新方案下考虑混凝土对称AN的几个族，我们探索了这种二维环境中的通用性边缘。在此基础上，我们开发了一种基于网络胶合操作的证明技术，