Year: 2008
Type: preprint
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 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.
Source: arXiv (Cornell University)
Authors: Dennunzio, Alberto, Guillon, Pierre, Masson, Benoît
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1626219174