Residual for Component Specifications

We address the problem of component reuse by describing a quotient operation. Starting from the specifications of the behaviors of the component and of the desired overall system, this operation computes the residual specification characteristic of the systems that, when composed with the given component, satisfy the overall specification. This problem is solved when behaviors are given by modal or acceptance specifications and when composition allows mixed product and internalization of events. We show on an example how weak form of liveness constraint may be taken into account by this technique.