A Visual Interpreter Semantics for Statecharts Based on Amalgamated Graph Transformation

Several different approaches to define the formal operational semantics of statecharts have been proposed in the literature, including visual techniques based on graph transformation. These visual approaches either define a compiler semantics (translating a concrete statechart into a semantical domain) or they define an interpreter using complex control and helper structures. Existing visual semantics definitions make it difficult to apply the classical theory of graph transformations to analyze behavioral statechart properties due to the complex control structures. In this paper, we define an interpreter semantics for statecharts based on amalgamated graph transformation where rule schemes are used to handle an arbitrary number of transitions in orthogonal states in parallel. We build on an extension of the existing theory of amalgamation from binary to multi-amalgamation including nested application conditions to control rule applications for automatic simulation. This is essential for the interpreter semantics of statecharts. The theory of amalgamation allows us to show termination of the interpreter semantics of well-behaved statecharts, and especially for our running example, a producer-consumer system.