因果图动力学
Causal graph dynamics
摘要：
我们将元胞自动机理论扩展到任意时变图。换句话说，我们形式化，并证明定理，直观的想法，一个标记的图，它在时间上的发展-但在自然的约束下，信息只能以有限的速度传输，相对于由图形给出的距离。也推广了平行不变性的概念。我们为这些“因果图动力学”提供的定义是简单和公理化的。我们提供的定理也表明它是鲁棒的。例如，因果图动力学在复合和半径1的限制下是稳定的。在有限的情况下，细胞自动机理论的一些基本事实仍然存在：因果图动力学承认连续函数的特征，并且它们在反演下是稳定的。所提供的例子表明了这个数学对象的广泛应用，从复杂系统科学到理论物理。关键词：动态网络，布尔网络，生成网络自动机，凯莱细胞自动机，图自动机，图重写自动机，并行图变换，合并图变换，时变图，Regge演算，局部，无信号。
英文摘要：
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that information can only ever be transmitted at a bounded speed, with respect to the distance given by the graph. The notion of translation-invariance is also generalized. The definition we provide for these "causal graph dynamics" is simple and axiomatic. The theorems we provide also show that it is robust. For instance, causal graph dynamics are stable under composition and under restriction to radius one. In the finite case some fundamental facts of Cellular Automata theory carry through: causal graph dynamics admit a characterization as continuous functions, and they are stable under inversion. The provided examples suggest a wide range of applications of this mathematical object, from complex systems science to theoretical physics. KEYWORDS: Dynamical networks, Boolean networks, Generative networks automata, Cayley cellular automata, Graph Automata, Graph rewriting automata, Parallel graph transformations, Amalgamated graph transformations, Time-varying graphs, Regge calculus, Local, No-signalling.
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。
