A Novel WCET Semantics of Synchronous Programs

Abstract

Abstract. Semantics for synchronous programming languages are well known. They capture the execution behaviour of reactive systems using precise formal operational or denotational models for verification and unambiguous semantics-preserving compilation. As synchronous programs are highly time critical, there is an imminent need for the development of an execution time aware semantics that can be used as the formal basis of WCET tools. To this end we propose such a compositional semantics for synchronous programs. Our approach, which is algebraic and based on formal power series in min-max-plus algebra, combines in one setting both the linear system theory for timing and constructive Gödel-Dummet logic for functional specification of synchronisation behaviour. The developed semantics is illustrated using a running example in the SCCharts language.

Compositional timing-aware semantics for synchronous programming

“…This section extends the results of [14] to model arbitrary hierarchical sequential-parallel control-flow. We call all primitive elements of a TCCFG, particularly signals and transitions, the controls.…”

“…It is precise (called (1, 0)-timing compositional in the terminology of [16]) because it combines both signaldependent function and timing, unlike [5], [11], [15] which also use max-plus algebra but abstract from signals. It is general because it captures arbitrary hierarchical structures of sequential and concurrent control flow, unlike [14] which also uses formal power series in min-max-plus algebra but is restricted flat parallel compositions of sequential synchronous automata. Observe that the TAP is non-trivial because of the multi-threading semantics of PRET-C.…”

“…For instance, to account for the timing costs of B2, B3 and B4 we would refine equation B3 = B2 ∨ XB4 to become B3 = (5 B2) ∨ XB4 and B4 = ¬S ∧ B3 to B4 = 10 (¬S ∧ 25 B3). Such WCRT modelling has been proposed in [14] for purely sequential control-flow, without fork/join and abort constructs, which we model here.…”

“…A unifying approach that would make it possible to integrate these various techniques systematically has recently been proposed based on formal power series in min-max-plus algebra [14]. This paper further investigates these algebraic techniques and makes the following contributions:…”

“…Existing modelling techniques only treat the flat parallel composition of sequential automata, e.g., [14], or are fully structural but do not have signals, e.g., [15]. • For signal-abstracted WCRT we present the first fully modular modelling approach, which can be directly implemented to generate a practical WCRT analysis algorithm.…”