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On the sofic limit sets of cellular automata

Published online by Cambridge University Press:  19 September 2008

Alejandro Maass
Affiliation:
Departamento de Ingeniería Matemática, Universidad de Chile, casilla 170/3, correo 3, Santiago, Chile(amaass@llaima.dim.uchile.cl)

Abstract

It is not known in general whether any mixing sofic system is the limit set of some one-dimensional cellular automaton. We address two aspects of this question. We prove first that any mixing almost of finite type (AFT) sofic system with a receptive fixed point is the limit set of a cellular automaton, under which it is attained in finite time. The AFT condition is not necessary: we also give examples of non-AFT sofic systems having the same properties. Finally, we show that near Markov sofic systems (a subclass of AFT sofic systems) cannot be obtained as limit sets of cellular automata at infinity.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1995

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