A compact topology for sand automata - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2008

A compact topology for sand automata

Résumé

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of the cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with the nilpotency. We show that the classical definition is not meaningful for sand automata. Then, we introduce a suitable new notion of nilpotency for sand automata. Finally, we prove that this simple dynamical behavior is undecidable.
Fichier principal
Vignette du fichier
nilpsa5_arxiv.pdf (273 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00259945 , version 1 (29-02-2008)

Identifiants

Citer

Alberto Dennunzio, Pierre Guillon, Benoît Masson. A compact topology for sand automata. 2008. ⟨hal-00259945⟩
203 Consultations
49 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More