Timed and Hybrid Statecharts and Their Textual Representation

y Abstract. A structured operational semantics is presented for Timed and Hybrid Statecharts, which are generalizations of the visual speciication language of Statecharts intended to model real-time and hybrid systems. In order to study some of the basic features of Statecharts and the extensions necessary to treat real-time and continuous behaviors without being distracted by the graphical representation, we introduce a concurrent real-time language that can be viewed as a textual representation of Statecharts. The language contains statements for delays, preemption, and timeouts. A struc-tured operational semantics of the language and an illustrative example of its use for speciication are presented. Extensions to the speciication of hybrid systems are obtained by allowing a diierential equation as a statement of the extended language. Structured operational semantics is also given for the hybrid version. The same extensions are then applied to the visual Statechart language, and similar compositional semantics are deened.