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Cellular Automata and Kan Extensions
arXiv - CS - Distributed, Parallel, and Cluster Computing Pub Date : 2021-02-24 , DOI: arxiv-2102.12156
Alexandre FernandezLACL, Luidnel MaignanLACL, Antoine SpicherLACL

In this paper, we formalize precisely the sense in which the application of cellular automaton to partial configuration is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the two possible ways to do such an extension and the ingredients involved in their definition are related through Kan extensions in many ways. These relations provide additional links between computer science and category theory, and also give a new point of view on the famous Curtis-Hedlung theorem of cellular automata from the extended topological point of view provided by category theory. These relations provide additional links between computer science and category theory. No prior knowledge of category theory is assumed.

中文翻译:

元胞自动机和Kan扩展

在本文中,我们精确地形式化了这样一种意义,即通过Kan扩展的分类概念,将细胞自动机应用于部分配置是其局部转移函数的自然扩展。实际上,进行这种扩展的两种可能方法及其定义所涉及的要素在许多方面都通过Kan扩展而相关。这些关系为计算机科学和类别理论之间提供了额外的联系,并且从类别理论提供的扩展拓扑观点出发,也为著名的元胞自动机的Curtis-Hedlung定理提供了新的观点。这些关系在计算机科学和类别理论之间提供了其他联系。假定没有类别理论的先验知识。
更新日期:2021-02-25
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