A characterization of $p$-automatic sequences as columns of linear cellular automata
arXiv:1209.6008 · doi:10.1016/j.aam.2014.10.002
Abstract
We show that a sequence over a finite field $\mathbb F_q$ of characteristic $p$ is $p$-automatic if and only if it occurs as a column of the spacetime diagram, with eventually periodic initial conditions, of a linear cellular automaton with memory over $\mathbb F_q$. As a consequence, the subshift generated by a length-$p$ substitution can be realized as a topological factor of a linear cellular automaton.
19 pages, 6 figures; final version