On the reversibility and the closed image property of linear cellular automata release_r2vt7pnkhzf2bklqtfim4yddna

by Tullio Ceccherini-Silberstein, Michel Coornaert

Released as a article .

2010  

Abstract

When G is an arbitrary group and V is a finite-dimensional vector space, it is known that every bijective linear cellular automaton τ V^G → V^G is reversible and that the image of every linear cellular automaton τ V^G → V^G is closed in V^G for the prodiscrete topology. In this paper, we present a new proof of these two results which is based on the Mittag-Leffler lemma for projective sequences of sets. We also show that if G is a non-periodic group and V is an infinite-dimensional vector space, then there exist a linear cellular automaton τ_1 V^G → V^G which is bijective but not reversible and a linear cellular automaton τ_2 V^G → V^G whose image is not closed in V^G for the prodiscrete topology.
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Type  article
Stage   accepted
Date   2010-09-21
Version   v2
Language   en ?
arXiv  0910.0863v2
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