On Symbolic Representations of One-dimensional Cellular Automata
Junbiao Guan and Fangyue Chen
We associate a one-dimensional cellular automaton with a unit interval map, and show that if the unit interval map is expansive, then we could find a symbolic representation of a cellular automaton under the framework of usual symbolic dynamics system. If the unit interval map is not expansive, then we could find a symbolic representation of a cellular automaton under the framework of general symbolic dynamics system. We investigate symbolic representations of cellular automata in two different metric topologies, and analyze the relation between them as well.
Keywords: Symbolic representation; expansive map; cellular automaton; symbolic dynamics.