Ethan M. Coven, William Geller, Sylvia Silberger, and William P. Thurston
\define \PP{\mathcal P} {A finite collection~$\PP$ of finite sets {\it tiles the integers\/} iff the integers can be expressed as a disjoint union of translates of members of $\PP$. We associate with such a tiling a doubly infinite sequence with entries from~$\PP$. The set of all such sequences is a sofic system, called a {\it tiling system}. We show that, up to powers of the shift, every shift of finite type can be realized as a tiling system.}