A compact topology for sand automata

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A compact topology for sand automata
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.
Alberto Dennunzio, Pierre Guillon, Benoît Ma
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Alberto Dennunzio, Pierre Guillon, Benoît Masson
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