Sand automata as cellular automata

  • Authors:

  • Alberto Dennunzio;Pierre Guillon;Benoît Masson

  • Affiliations:

  • Università degli studi di Milano-Bicocca, Dipartimento di Informatica Sistemistica e Comunicazione, viale Sarca 336, 20126 Milano, Italy;Université Paris-Est, Laboratoire dInformatique de lInstitut Gaspard Monge, UMR CNRS 8049, 5 bd Descartes, 77454 Marne la Vallée Cedex 2, France;Laboratoire dInformatique Fondamentale de Marseille (LIF)-CNRS, Aix-Marseille Université, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

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 cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with simple sand automata. We show that the classical definition of nilpotency is not meaningful for sand automata. Then, we introduce the suitable new notion of flattening sand automata. Finally, we prove that this simple dynamical behavior is undecidable.