Behavior Consistent Refinement of Object Life Cycles

This paper examines the inheritance of object life cycles that are specified by behavior diagrams. A behavior diagram of an object type models possible life cycles of its instances by states, activities and arcs corresponding to places, transitions and arcs of Petri Nets. In an inheritance hierarchy, subtypes specialize the life cycle of supertypes by extension, i.e., adding states and activities, and (the focus of this paper) refinement, i.e., decomposing states and activites into substates and subactivities.

The main contribution of this paper are necessary and sufficient rules for checking behavior consistency between a behavior diagram of a type and a refined subtype, as well as for the combination of extension and refinement.