Cellular Automata and Kan Extensions

Alexandre Fernandez (1) , Luidnel Maignan (1) , Antoine Spicher (1)

1 LACL - Laboratoire d'Algorithmique Complexité et Logique

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.

Domaines: Systèmes dynamiques [math.DS]; Automates cellulaires et gaz sur réseau [nlin.CG]; Catégories et ensembles [math.CT]; Calcul parallèle, distribué et partagé [cs.DC]; Système multi-agents [cs.MA]; Modélisation et simulation

Alexandre Fernandez, Luidnel Maignan, Antoine Spicher. Cellular Automata and Kan Extensions. [Research Report] Univ Paris Est Creteil, LACL, 94000, Creteil, France. 2021. ⟨hal-03149398v2⟩