Post-surjectivity and balancedness of cellular automata over groups
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.
Cite
@article{arxiv.1507.02472,
title = {Post-surjectivity and balancedness of cellular automata over groups},
author = {Silvio Capobianco and Jarkko Kari and Siamak Taati},
journal= {arXiv preprint arXiv:1507.02472},
year = {2023}
}
Comments
16 pages, 3 figures, LaTeX "dmtcs-episciences" document class. Final version for Discrete Mathematics and Theoretical Computer Science. Prepared according to the editor's requests