  The class of periodic-finite-type shifts (PFT's) is a class of sofic shifts
that strictly includes the class of shifts of finite type (SFT's), and the zeta
function of a PFT is a generating function for the number of periodic sequences
in the shift. In this paper, we derive a useful formula for the zeta function
of a PFT. This formula allows the zeta function of a PFT to be computed more
efficiently than the specialization of a formula known for a generic sofic
shift
