Cellular Automata and Kan Extensions - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2021

Cellular Automata and Kan Extensions

Résumé

In this paper, we formalize precisely the sense in which the application of a cellular automaton to partial configurations 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-Hedlund theorem of cellular automata from the extended topological point of view provided by category theory. These links also allow to relatively easily generalize concepts pioneered by cellular automata to arbitrary kinds of possibly evolving spaces. No prior knowledge of category theory is assumed.
Fichier non déposé

Dates et versions

hal-03938172 , version 1 (13-01-2023)

Identifiants

Citer

Alexandre Fernandez, Luidnel Maignan, Antoine Spicher. Cellular Automata and Kan Extensions. 27th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2021), Alonso Castillo-Ramirez; Pierre Guillon; Kévin Perrot, Jul 2021, Marseille (CIRM, Centre International de Rencontres Mathématiques), France. pp.7:1--7:12, ⟨10.4230/OASIcs.AUTOMATA.2021.7⟩. ⟨hal-03938172⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More