Abstract-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 ACðP Þ, 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 ACðP Þ 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 ACðP Þ used to symbolically simplify and handle connectors. We provide examples illustrating applications of ACðP Þ, including a general component model encompassing methods for incremental model decomposition and efficient implementation by using symbolic techniques.

Abstract. Comparison between different formalisms and models is often by flattening structure and reducing them to behaviorally equivalent models e.g., automaton and Turing machine. This leads to a notion of expressiveness which is not adequate for component-based systems where separation between behavior and coordination mechanisms is essential. The paper proposes a notion of glue expressiveness for component-based frameworks characterizing their ability to coordinate components. Glue is a closed under composition set of operators mapping tuples of behavior into behavior. Glue operators preserve behavioral equivalence. They only restrict the behavior of their arguments by performing memoryless coordination. Behavioral equivalence induces an equivalence on glue operators. We compare expressiveness of two glues G 1 and G 2 by considering whether glue operators of G 1 have equivalent ones in G 2 (strong expressiveness). Weak expressiveness is defined by allowing a finite number of additional behaviors in the arguments of operators of G 2 . We propose an SOS-style definition of glues, where operators are characterized as sets of SOS-rules specifying the transition relation of composite components from the transition relations of their constituents. We provide expressiveness results for the glues of BIP and of process algebras such as CCS, CSP and SCCS. We show that for the considered expressiveness criteria, glues of the considered process calculi are less expressive than general SOS glue. Furthermore, glue of BIP has exactly the same strong expressiveness as glue definable by the SOS characterization.

The Algebra of Connectors AC(P ) is used to model structured interactions in the BIP component framework. Its terms are connectors, relations describing synchronization constraints between the ports of component-based systems. Connectors are structured combinations of two basic synchronization protocols between ports: rendezvous and broadcast.In a previous paper, we have studied interaction semantics for AC(P ) which defines the meaning of connectors as sets of interactions. This semantics reduces broadcasts into the set of their possible interactions and thus blurs the distinction between rendezvous and broadcast. It leads to exponentially complex models that cannot be a basis for efficient implementation. Furthermore, the induced semantic equivalence is not a congruence.For a subset of AC(P ), we propose a new causal semantics that does not reduce broadcast into a set of rendezvous and explicitly models the causal dependency relation between triggers and synchrons. The Algebra of Causal Trees CT (P ) formalizes this subset. It is the set of the terms generated from interactions on the set of ports P , by using two operators: a causality operator and a parallel composition operator. Terms are sets of trees where the successor relation represents causal dependency between interactions: an interaction can participate in a global interaction only if its father participates too. We show that causal semantics is consistent with interaction semantics. Furthermore, it defines an isomorphism between CT (P ) and the set of the terms of AC(P ) involving triggers.Finally, we define for causal trees a boolean representation in terms of causal rules. This representation is used for their manipulation and simplification as well as for synthesizing connectors.How to cite this report:

We study a framework for the specification of architecture styles as families of architectures involving a common set of types of components and coordination mechanisms. The framework combines two logics: 1) interaction logics for the specification of architectures as generic coordination schemes involving a configuration of interactions between typed components; and 2) configuration logics for the specification of architecture styles as sets of interaction configurations. The presented results build on previous work on architecture modelling in BIP. We show how propositional interaction logic can be extended into a corresponding configuration logic by adding new operators on sets of interaction configurations. In addition to the usual set-theoretic operators, configuration logic is equipped with a coalescing operator + to express combination of configuration sets. We provide a complete axiomatization of propositional configuration logic as well as decision procedures for checking that an architecture satisfies given logical specifications. To allow genericity of specifications, we study first-order and second-order extensions of the propositional configuration logic. First-order logic formulas involve quantification over component variables. Second-order logic formulas involve additional quantification over sets of components. We provide several examples illustrating the application of the results to the characterisation of various architecture styles. We also provide an experimental evaluation using the Maude rewriting system to implement the decision procedure for the propositional flavour of the logic.