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

Tullio Ceccherini-Silberstein, Michel Coornaert
2011 Theoretical Computer Science  
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
more » ... 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.
doi:10.1016/j.tcs.2010.09.020 fatcat:2wct3xu6xfbr7mgpgmq3qm4hou