  We discuss a method of calculating the zeta function of subshifts which have
a presentation by a finite directed graph labeled by elements of the associated
inverse semigroup. This class of subshifts is introduced as a class of property
A subshifts(T.Hamachi, K.Inoue and W.Krieger/Subsystems of finite type and
semigroup invariants of subshifts, preprint), and the Dyck shift and the
Motzkin shift are representative subshifts in this class. The exact number of
the periodic points and entropies are also given by this method, and these
values are used in the embedding condition for an irreducible shift of finite
type into a subshift in this class.
