Path sets in one-sided symbolic dynamics

Abstract Path sets are spaces of one-sided infinite symbol sequences associated to pointed graphs ( G , v 0 ) , which are edge-labeled directed graphs with a distinguished vertex v 0 . 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.

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