THE SYMBOLIC DYNAMICS OF TILING THE INTEGERS

ETHAN M. COVEN WILLIAM GELLER SYLVIA SILBERGER AND WILLIAM P. THURSTON

Abstract. A finite collection P of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of P. We associate with such a tiling a doubly infinite sequence with entries from 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.