Path sets in one-sided symbolic dynamics

Path sets are spaces of one-sided infinite symbol sequences associated to pointed graphs (G,v0)(G,v0), which are edge-labeled directed graphs with a distinguished vertex v0v0. Such sets arise naturally as address labels in geometric fractal constructions and in other contexts. The resulting set of symbol sequences need not be closed under the one-sided shift. This paper establishes basic properties of the structure and symbolic dynamics of path sets, and shows that they are a strict generalization of one-sided sofic shifts.