On the Syntax and Semantics of State Machines

Within Model Driven Development (MDD), state machines are a common mechanism for modelling behaviour. The development of a formal semantics for state machines continues to be a very active and important area of research, because the development of interoperating MDD tools requires a precise, unambiguous, yet readable account of the meaning of the diagrams. Research on state machine semantics is severely complicated by the fact that there are multiple suggested approaches to formalizing state machine semantics. In addition, there are currently several well-documented state machine dialects, each subtly different from the others. According to the research literature, the most popular state machine dialects are classical and Rhapsody statecharts and UML state machine diagrams. These three dialects appear to be very similar; however, there are several key syntactic and semantic differences. The first half of this paper presents the results of a comparative study of these three dialects with the help of several illustrative examples. We also present a classification of the differences, together with a comprehensive overview. The second half of this paper is the result of a comparative literature review on approaches to formally capture the semantics of UML state machines; it categorizes and compares 26 different approaches. As a primary categorization, we use the underlying formalism of the approaches, e.g., mathematical models, rewriting systems and translation approaches. We also compare the approaches along several secondary dimensions, such as coverage of state machine features, analysis and tool support.