Synthesizing Controllers from Duration Calculus

Duration Calculus, as introduced in ZHR91], is a logic for reasoning about requirements for real-time systems at a high level of abstraction from operational detail, which qualiies it as an interesting starting point for embedded controller design. Such a design activity is generally thought to aim at a control device the physical behaviours of which satisfy the requirements formula, i.e. the reenement relation between requirements and implementations is taken to be trajectory inclusion. Due to the abstractness of the vocabulary of Duration Calculus, trajectory inclusion between control requirements and controller designs is undecidable even for fully synchronous controllers, rendering automatic veriication and automatic synthesis impossible wrt. trajectory inclusion. In this paper, besides reviewing these results, we are giving evidence that trajectory inclusion is in general an overly restrictive reenement relation for embedded controller design and exploit this fact for developing an automatic procedure for controller synthesis from speciications formalized in Duration Calculus. As far as we know, this is the rst positive result concerning feasibility of automatic synthesis from dense-time Duration Calculus.