  Building on previous work by the author and Robin Deeley, we give a thorough
presentation of the techniques developed for synchronizing dynamical systems in
the special case of synchronizing shift spaces. Following work of Thomsen, we
give a construction of the homoclinic and heteroclinic $C^\ast$-algebras of a
shift space in terms of Bratteli diagrams. Lastly we present several specific
examples which demonstrate these techniques. For the even shift we give a
complete computation of all the associated invariants. We also present an
example of a strictly non-sofic synchronizing shift. In particular we discuss
the rank of the $K$-theory of the homoclinic algebra of a shift space and its
implications. We also give a construction for producing from any minimal shift
a synchronizing shift whose set of non-synchronizing points is exactly the
original minimal shift.
