Behavioral Refinement and Compatibility of Statechart Extensions

We compare the notions of refinement and compatibility for system models and their variants described as statecharts. Compatibility, in the sense of substitutability, means that a system can be used in any place where the original one was used. We show that existing definitions of refinement and compatibility are orthogonal, if they include an interface extension. Then, we focus on extended compatibility, which means that the system returns to a compatible behavior after some time even if the newly added features are used. Our new result shows under what conditions the usage of a newly added feature preserves behavior. More specifically, we perform a novel kind of elimination of the newly added behavior on a trace level. In this way, we can achieve extended compatibility even if the newly added features use existing input and output events, which is not possible with existing abstractions and refinement concepts.