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arXiv · 1507.02472

Post-surjectivity and balancedness of cellular automata over groups

Silvio Capobianco·Jarkko Kari·Siamak Taati
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Abstract

We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injective, post-surjective cellular automata are reversible. Moreover, on sofic groups, post-surjectivity alone implies reversibility. We also prove that reversible cellular automata over arbitrary groups are balanced, that is, they preserve the uniform measure on the configuration space.

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Silvio Capobianco, Jarkko Kari, Siamak Taati. 2015-07-09. Post-surjectivity and balancedness of cellular automata over groups. https://doi.org/10.23638/dmtcs-19-3-4

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