Emergent Mind
A characterization of $p$-automatic sequences as columns of linear cellular automata
(1209.6008)
Published Sep 26, 2012
in
math.DS
,
cs.FL
,
and
nlin.CG
Abstract
We show that a sequence over a finite field $\mathbb Fq$ 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 $\mathbb Fq$. 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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