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Abstract
A connection is made between the description of one-dimensional cellular automata as dynamical systems acting on a compact metric space, and as computational systems acting on strings. Operators are defined which determine a bijective correspondence between subshifts of infinite configurations and languages of finite strings. Under this correspondence, families of languages give rise to families of subshifts. Regular languages correspond to sofic subshifts. Families of subshifts corresponding to context-free, context-sensitive, and recursively enumerable languages are introduced and their closure properties under forward and backward cellular automaton images studied.
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