A characterization of p-automatic sequences as columns of linear cellular automata

Rowland, Eric and Yassawi, Reem (2015). A characterization of p-automatic sequences as columns of linear cellular automata. Advances in Applied Mathematics, 63 pp. 68–89.

DOI: https://doi.org/10.1016/j.aam.2014.10.002

Abstract

We show that a sequence over a finite field 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 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.

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