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The Algebra of Connectors - Structuring Interaction in BIP

We provide an algebraic formalization of connectors in the BIP component framework. A connector relates a set of typed ports. Types are used to describe different modes of synchronization, in particular, rendezvous and broadcast. Connectors on a set of ports P are modeled as terms of the algebra AC(P), generated from P by using a binary fusion operator and a unary typing operator. Typing associates with terms (ports or connectors) synchronization types - trigger or synchron - that determine modes of synchronization. Broadcast interactions are initiated by triggers. Rendezvous is a maximal interaction of a connector that includes only synchrons. The semantics of AC(P) associates with a connector the set of its interactions. It induces on connectors an equivalence relation which is not a congruence as it is not stable for fusion. We provide a number of properties of AC(P) used to symbolically simplify and handle connectors. We provide examples illustrating applications of AC(P), including a general component model encompassing methods for incremental model decomposition and efficient implementation by using symbolic techniques.