Undecidability of the Global Fixed Point Attractor Problem on Circular Cellular Automata
نویسندگان
چکیده
A great amount of work has been devoted to the understanding of the long time behavior of cellular automata CA As for any other kind of dynamical system the long time behavior of a CA is described by its attractors In this context it has been proved that it is undecidable to know whether every circular con guration of a given CA evolves to some xed point not unique In this paper we prove that it remains undecidable to know whether every circular con guration of a given CA evolves to the same xed point Our proof is based on properties concerning NW deterministic periodic tilings of the plane As a corollary it is concluded the already proved undecidability of the periodic tiling problem nevertheless our approach could also be used to prove this result in a direct and very simple way
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