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

Reachability in Cooperating Systems with Architectural Constraints is PSPACE-Complete