287 research outputs found
Limit sets of stable Cellular Automata
We study limit sets of stable cellular automata standing from a symbolic
dynamics point of view where they are a special case of sofic shifts admitting
a steady epimorphism. We prove that there exists a right-closing
almost-everywhere steady factor map from one irreducible sofic shift onto
another one if and only if there exists such a map from the domain onto the
minimal right-resolving cover of the image. We define right-continuing
almost-everywhere steady maps and prove that there exists such a steady map
between two sofic shifts if and only if there exists a factor map from the
domain onto the minimal right-resolving cover of the image. In terms of
cellular automata, this translates into: A sofic shift can be the limit set of
a stable cellular automaton with a right-closing almost-everywhere dynamics
onto its limit set if and only if it is the factor of a fullshift and there
exists a right- closing almost-everywhere factor map from the sofic shift onto
its minimal right- resolving cover. A sofic shift can be the limit set of a
stable cellular automaton reaching its limit set with a right-continuing
almost-everywhere factor map if and only if it is the factor of a fullshift and
there exists a factor map from the sofic shift onto its minimal right-resolving
cover. Finally, as a consequence of the previous results, we provide a
characterization of the Almost of Finite Type shifts (AFT) in terms of a
property of steady maps that have them as range.Comment: 18 pages, 3 figure
La biblioteca un agente social para el desarrollo de la lectura : Centro Cultural de España, Santiago, Chile, octubre de 2013
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