Technical Reports

Simon Bliudze, Joseph Sifakis
The Algebra of Connectors -- Structuring Interaction in BIP (2007)


Keywords: the algebra of connectors, interactions, component coordination, equivalence of connectors, transformation of connectors

Abstract: We provide an algebraic formalisation of {em connectors} in BIP. These are used to structure {em interactions} in a component-based system. A connector relates a set of typed ports. Types are used to describe different modes of synchronisation: rendezvous and broadcast, in particular. Connectors on a set of ports $P$ are modelled as terms of the algebra $AC(P)$, generated from $P$ by using an $n$-ary {em fusion} operator and a unary {em typing} operator. Typing associates with terms (ports or connectors) synchronisation types -- {em trigger} or {em synchron} --, which determine modes of synchronisation. Broadcast interactions are initiated by triggers. Rendezvous is a maximal interaction of a connector including 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 synchrony, methods for incremental model decomposition, and efficient implementation by using symbolic techniques.

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