  The reachability problem in cooperating systems is known to be
PSPACE-complete. We show here that this problem remains PSPACE-complete when we
restrict the communication structure between the subsystems in various ways.
For this purpose we introduce two basic and incomparable subclasses of
cooperating systems that occur often in practice and provide respective
reductions. The subclasses we consider consist of cooperating systems the
communication structure of which forms a line respectively a star.
