Stable Dynamics of Sand Automata

Alberto Dennunzio (1) , Pierre Guillon (2) , Benoît Masson (3)

1 DISCo - Dipartimento di Informatica Sistemistica e Comunicazione
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

In this paper, we study different notions of stability of sand automata, dynamical systems inspired by sandpile models and cellular automata. First, we study the topological stability properties of equicontinuity and ultimate periodicity, proving that they are equivalent. Then, we deal with nilpotency. The classical definition for cellular automata being meaningless in that setting, we define a more suitable one. Finally, we prove that this simple dynamical behavior is undecidable.

Domaines: Algorithme et structure de données [cs.DS]

Alberto Dennunzio, Pierre Guillon, Benoît Masson. Stable Dynamics of Sand Automata. 5th IFIP Conference on Theoretical Computer Science (TCS'08), Sep 2008, Milano, Italy, Italy. pp.157-169. ⟨hal-00620302⟩