We define a formal semantics of the combined use of UML 2 state machines, activities and interactions using Abstract State Machines. The behaviour of software models can henceforth be specified by composing these diagrams, choosing the most adequate formalism at each level of abstraction. We present several reasonable ways to link different kinds of diagrams and illustrate them by examples. We also give a formal semantics of communication between these diagrams. The resulting rules reveal unclear parts of the UML specification and serve as a basis for tool support.
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