Periodic-finite-type shift spaces

We introduce the class of periodic-finite-type (PFT) shift spaces. They are the subclass of shift spaces defined by a finite set of periodically forbidden words. Examples of PFT shifts arise naturally in the context, of distance-enhancing codes for partial-response channels. We show that the set of PFT shift spaces properly contains the set of finite-type shift spaces and is properly contained in the set of almost-finite-type shift spaces. We prove several properties of labeled graphs that present PFT shifts. For a given PFT shift, space, we identify a finite set of forbidden words-referred to as "periodic first offenders"-that define the shift space and that satisfy certain minimality properties. Finally, we present an efficient algorithm for constructing labeled graphs that present PFT shift spaces.