A Pragmatic Behavior Subtyping Relation Based on Both States and Actions

A behavior preserving relation betweenPetri-net systems is introduced in this paper, based on theobservability of both places and transitions, which is important inmodeling the dynamic behavior of concurrent object-oriented systems withPetri nets. Each group of closely related attributes of a concurrentobject is modeled by the state of a collection of observable places, andeach of its methods by a group of observable transitions. The groupingdistinguishes the definition in this paper from others, which makes iteasy to work together with the static object models, to reuse the modelsand to dispel the interference among groups, thus relieving the problemof inheritance anomaly by the possibility of dividing thesynchronization code into independent parts. For a formal definition ofthis behavior subtyping relation, Elementary Net systems, with bothS-elements and T-elements labeled, are used. Then it is extendedinformally to the state based coloured Petri net systems. Finally, thebackground of the definitions and the future work are presented.