  We show that certain C*-algebras which have been studied among others by
Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving
transformation of a measure space and/or to a covering map of a compact space
are special cases of the endomorphism crossed-product construction recently
introduced by the first named author. As a consequence these algebras are given
presentations in terms of generators and relations. These results come as a
consequence of a general Theorem on faithfulness of representations which are
covariant with respect to certain circle actions. For the case of topologically
free covering maps we prove a stronger result on faithfulness of
representations which needs no covariance. We also give a necessary and
sufficient condition for simplicity.
