Recursive Cellular Automata Invariant Sets

A bstract. Subshift s of bi-infinit e words give rise to languages in a natural way. Three invariant subshifts associated wit h cellular automata dynamics are considered : the periodic set, non-wandering set , and limit set . Exam ples have been given (see [8,12]) of cellular automata whose invarian t sets give rise to nonrecursive languages. In this pap er , examples are given of cellular aut omata whose invariant set s correspond to regular, context-free, and context-sensit ive languages. It is proved that a cellular automaton has a subshift of finite type limit set only if its images stabilize. As a corollary, only mixing subshifts of finite type can occur as cellular automaton limit sets.