Specifying Safety-Critical Systems with a Decidable Interval Temporal Logic

Punctual timing constraints are important in formal modeling of safety-criticalreal-time systems. But they are very expensive to express in dense time. Inmost cases, punctuality and dense-time lead to undecidability. E↵orts havebeen successful to obtain decidability; but the results are either non-primitiverecursive or nonelementary. In this paper we propose an interval temporal logicwhich can express quantitative temporal constraints and punctuality timing con-straints over continuous intervals and has a reasonable complexity. Our logicallows most specifications that are interesting in practice, and retains punctu-ality. It can capture the semantics of both events and states, and incorporatesthe notions duration and accumulation. We call this logic ESDL (the acronymstands for Eventand State-based Duration Logic). We show that the satis-fiability problem is decidable, and the complexity of the satisfiability problemis NEXPTIME. ESDL is one of a few decidable interval temporal logics withmetric operators. Through some case studies, we also show that ESDL canspecify many safety-critical real-time system properties which were previouslyspecified by undecidable interval logics or their decidable reductions based onsome abstractions.