Equivalences of Statecharts

We present a new semantics of Statecharts that excludes failures and a compositional formulation of this semantics based on Labelled Transition Systems (LTS). We consider a hierarchy of LTS equivalences and we study their congruence properties w.r. to statechart operators. 1 I n t r o d u c t i o n Statecharts are a specification language for reactive systems, introduced originally in [4]. The Statecharts formalism belongs to the family of synchronous languages including also, for instance, Esterel [2] and Argos [6]. Statecharts are finite state machines having the appeal of visual formalisms such as statetransition diagrams and Petri nets, but unlike either of these, they offer facilities of hierarchical structuring of states and modularity, which allow high level description and stepwise development. Now when dealing with large specifications, conciseness is an important issue. It may be useful to be able to substitute specifications with equivalent more concise ones. In general, one wants to be able to interchange subsystems proved to be behaviourally equivalent. In the case of statecharts, one is interested in considering equivalent two statecharts that do not differ as regards input-output sequences of signals and their causal dependencies. We define a new semantics of statecharts that differs from the one defined in [8] insofar as in our case the semantics of a statechart is always defined. Next, following [9] (see also [10]), we represent statecharts by terms and we give a compositional semantics of statecharts by translating statechart terms into labelled transition systems (LTS). The agreement of the two semantics can be proved. Then we define equivalence of two statecharts as isomorphism of the respective LTS's. As this equivalence is too strong, we consider LTS equivalences studied in [3] and we investigate their congruence properties with respect to statechart and-composition and or-composition. 2 S t a t e c h a r t t e r m s Statecharts are a visual specification formalism which enriches state-transition diagrams by a tree-like structuring of states (leaves of such trees are called * Research partially supported by Esprit BRA 8130 LOMAPS.