A Pragmatic Behavior Subtyping Relation Based on Both States and Actions

A behavior preserving relation between Petri-net systems is introduced in this paper, based on the observability of both places and transitions, which is important in mod-eling the dynamic behavior of concurrent object-oriented systems with Petri nets. Each group of closely related attributes of a concurrent object is modeled by the state of a collection of observable places, and each of its methods by a group of observable transitions. The grouping distinguishes the definition in this paper from others, which makes it easy to work together with the static object models, to reuse the models and to dispel the interference among groups, thus relieving the problem of inheritance anomaly by the possibility of dividing the synchroniza-tion code into independent parts. For a formal definition of this behavior subtyping relation, Elementary Net systems, with both S-elements and T-elements labeled, are used. Then it is extended informally to the state based coloured Petri net systems. Finally, the background of the definitions and the future work are presented.