  We introduce MSO graph storage types, and call a storage type MSO-expressible
if it is isomorphic to some MSO graph storage type. An MSO graph storage type
has MSO-definable sets of graphs as storage configurations and as storage
transformations. We consider sequential automata with MSO graph storage and
associate with each such automaton a string language (in the usual way) and a
graph language; a graph is accepted by the automaton if it represents a correct
sequence of storage configurations for a given input string. For each MSO graph
storage type, we define an MSO logic which is a subset of the usual MSO logic
on graphs. We prove a B\"uchi-Elgot-Trakhtenbrot theorem, both for the string
case and the graph case. Moreover, we prove that (i) each MSO graph
transduction can be used as storage transformation in an MSO graph storage
type, (ii) every automatic storage type is MSO-expressible, and (iii) the
pushdown operator on storage types preserves the property of
MSO-expressibility. Thus, the iterated pushdown storage types are
MSO-expressible.
