In this paper, we study different notions of stability for 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 dynamical behavior is undecidable.

Dennunzio, A., Guillon, P., Masson, B. (2008). Stable dynamics of sand automata. In Fifth IFIP International Conference on Theoretical Computer Science IFIP - TCS 2008 (pp.157-169). Springer [10.1007/978-0-387-09680-3].

Stable dynamics of sand automata

Dennunzio, A;
2008

Abstract

In this paper, we study different notions of stability for 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 dynamical behavior is undecidable.
paper
sand automata, stability, undecidability
English
IFIP International Conference on Theoretical Computer Science held at the 20th World Computer Congress SEP 07-10
2008
Fifth IFIP International Conference on Theoretical Computer Science IFIP - TCS 2008
978-0-387-09679-7
2008
273
157
169
none
Dennunzio, A., Guillon, P., Masson, B. (2008). Stable dynamics of sand automata. In Fifth IFIP International Conference on Theoretical Computer Science IFIP - TCS 2008 (pp.157-169). Springer [10.1007/978-0-387-09680-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/14826
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