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arXiv · 0906.0857

2D cellular automata: dynamics and undecidability

Enrico Formenti·Alberto Dennunzio·Michael Weiss
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Abstract

In this paper we introduce the notion of quasi-expansivity for 2D CA and we show that it shares many properties with expansivity (that holds only for 1D CA). Similarly, we introduce the notions of quasi-sensitivity and prove that the classical dichotomy theorem holds in this new setting. Moreover, we show a tight relation between closingness and openness for 2D CA. Finally, the undecidability of closingness property for 2D CA is proved.

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Enrico Formenti, Alberto Dennunzio, Michael Weiss. 2009-09-29. 2D cellular automata: dynamics and undecidability. https://arxiv.org/abs/0906.0857

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