  A construction of Crochemore, Mignosi and Restivo in the automata theory
literature gives a presentation of a finite-type constrained system (FTCS) that
is deterministic and has a relatively small number of states. This construction
is thus a good starting point for determining the minimal deterministic
presentation, known as the Shannon cover, of an FTCS. We analyze in detail the
Crochemore-Mignosi-Restivo (CMR) construction in the case when the list of
forbidden words defining the FTCS is of size at most two. We show that if the
FTCS is irreducible, then an irreducible presentation for the system can be
easily obtained by deleting a prescribed few states from the CMR presentation.
By studying the follower sets of the states in this irreducible presentation,
we are able to explicitly determine the Shannon cover in some cases. In
particular, our results show that the CMR construction directly yields the
Shannon cover in the case of an irreducible FTCS with exactly one forbidden
word, but this is not in general the case for FTCS's with two forbidden words.
