  We introduce two algebras associated with a subshift over an arbitrary
alphabet. One is unital and the other not necessarily. We focus on the unital
case and describe a conjugacy between Ott-Tomforde-Willis subshifts in terms of
a homeomorphism between the Stone duals of suitable Boolean algebras, and in
terms of a diagonal-preserving isomorphism of the associated unital algebras.
For this, we realise the unital algebra associated with a subshift as a
groupoid algebra and as a partial skew group ring.
