On the Compositional Properties of UML Statechart Diagrams

This paper proposes a revised semantic interpretation of UML Statechart Diagrams which ensures, under the specified design rules, that Statecharts may be constructed to have true compositional properties. In particular, hierarchical state machines may be properly encapsulated to allow independent verification and compositional testing, something which is not possible under the current UML semantics. Certain problems regarding the formal tractability of UML Satechart Diagrams are addressed, such as the confusion over states and connectors, the flattening effect of boundary-crossing transitions, and the consequences of inverting the inter-level priority rule for handling concurrent events. A set-theoretic formal treatment of object states, events, guards and run-tocompletion processing is given, describing both serial and concurrent Statecharts.