Veriication of Temporal and Real-time Properties of Statecharts

This thesis is concerned with the formal veri cation of statecharts. Statecharts area synchronous formalism for the speci cation of reactive systems that is obtainedby introducing in classical state-transition diagrams notions of hierarchy, parallelismand communication. Propositional -calculus is a very convenient formalism for ex-pressing the properties characterizing the correctness of statecharts. Compositionalveri cation is essential for supporting stepwise development of correct speci cations.A necessary step to realize it is a compositional semantics. We de ne a composi-tional labelled transition system semantics for statecharts, which agrees with thesemantics of Pnueli and Shalev. Such a semantics is obtained via a translation ofstatecharts into a process language, called SP , whose main feature is an operatorof process re nement. We de ne a compositional proof system for deciding whethera closed SP process satis es a -calculus formula, where techniques of local andcompositional model checking are combined in the style of [12].Statecharts as de ned originally are not adequate for the speci cation of real-time systems, where also the quantitative aspect of time must be considered. Wepropose an extension of statecharts and of the language SP with real-time featuresby assuming a discrete time domain. We generalize the Pnueli and Shalev semanticsto timed statecharts and we propose a semantics of timed SP processes as a discreteversion of timed graphs. A real-time discrete extension of -calculus called RTL isde ned for expressing properties characterizing the correctness of timed processes,and a proof system for checking whether a set of timed states of a timed graphsatis es an RTL formula is proposed. A generalization of the technique proposedby Winskel [92] is exploited for supporting local model checking. The proof systemprovides the basis for extending the compositional method for untimed processes totimed ones. AcknowledgementsFirst of all I wish to thank my supervisor Andrea Maggiolo-Schettini for its help andencouragment during these two years. I also thank Andrea Masini who introducedme to the eld of temporal and modal logics.Thanks to my external referees Mads Dam and Colin Stirling for their carefulreading of my thesis and for their comments and suggestions.