What Is in a Step: New Perspectives on a Classical Question

Abstract

Abstract. In their seminal 1991 paper "What is in a Step: On the Semantics of Statecharts", Pnueli and Shalev showed how, in the presence of global consistency and while observing causality, the synchronous language Statecharts can be given coinciding operational and declarative step semantics. Over the past decade, this semantics has been supplemented with order-theoretic, denotational, axiomatic and game-theoretic characterisations, thus revealing itself as a rather canonical interpretation of the synchrony hypothesis. In this paper, we survey these characterisations and use them to emphasise the close but not widely known relations of Statecharts to the synchronous language Esterel and to the field of logic programming. Additionally, we highlight some early reminiscences on Amir Pnueli's contributions to characterise the semantics of Statecharts.

Denotational fixed-point semantics for constructive scheduling of synchronous concurrency

“…Proving the soundness of causality analyses necessarily requires maintaining some form of refinement ("constructiveness" or "dependency") information about a lower-level asynchronous micro-step semantics. The first to observe this were Huizing et al [43] who showed that combining compositionality, causality and the Synchrony Hypothesis cannot be done within a single-levelled semantics (see also [24]). In other words, causality analysis establishes consistency of a synchronous macro-step with respect to an asynchronous micro-step execution model.…”

SCCharts: sequentially constructive statecharts for safety-critical applications

“…Various other approaches with their own admissible scheduling schemes have been considered for statecharts. The three most prominent approaches are due to Pnueli and Shalev [24,12], Boussinot [7] and Berry and Shiple [29,5]. None of them considers sequential control flow as SC does.…”