Component Substitutability via Equivalencies of Component-Interaction Automata

We provide a new look at formal aspects of component substitutability (replacement of a component with a new one) and independent implementability (reuse of a component in any system where its implementation satisfies the specification given by the environment), in view of an underlying formalism called Component-interaction automata. Our aim is to offer a formal characterization of preconditions that lead to reconfiguration correctness (proper component substitution and safe independent implementation). Such preconditions then guarantee that the updated system remains equivalent to the former one and hence there is no need to verify it again. The contribution of the paper is twofold. First, we formally define three relations that allows us to compare behaviours of two components with respect to reconfiguration correctness. Namely, the equivalence relation, specification-implementation relation, and substitutability relation. Second, we formally characterize the problem of component substitutability for both equivalent and non-equivalent components, and the problem of independent implementability. The characterizations are captured in several propositions which are proved in the text.