A Specification Theory for Reachability by Design

Modular design aims at building complex reactive systems by assembling components, possibly taken off-the-shelf. This approach can be supported by a specification theory in which requirements correspond to specifications while components are models of the specifications. In this article, we consider components which have to fulfill a reachability objective. A difficulty is then induced by the fact that reachability properties are not compositional. The approach we advocate consists in controlling the design flow of components, that is, the evolution of their specifications through combinations and refinements, in order to ensure a reachability property by construction. We define specifications in terms of marked acceptance specifications which are automata enriched with variability information encoded by acceptance sets and with reachability constraints. We then develop a specification theory with both logical and structural composition operators and with quotient, ensuring reachability properties by design.