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