Decision Procedures for Openness and Local Injectivity

Let F be a cellular automaton on the space of all sequences from a finite alphabet. From the local description of F a finite labeled digraph is constructed with a distinguished subdi graph. The surjectivity and openness of F are proved to correspond to properties of these digraphs. Similarly, another finite labeled digraph is constructed with a distin guished subset of its vert ex set . Th e injectivit y and local injectivity of F are proved to correspond to properties of this digraph and its subset . All the relevant prop erties can be checked in finitely many steps. Analogous results are also obta ined for biinfinite sequences,