# Causal Semantics for the Algebra of Connectors

## Abstract

The Algebra of Connectors Open image in new window is used to model structured interactions in the BIP component framework. Its terms are *connectors*, i.e. 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*. They are generated from the ports of *P* by using a binary *fusion* operator and a unary *typing* operator. Typing associates with terms (ports or connectors) synchronization types: *trigger* or *synchron*.

In a previous paper, we studied interaction semantics for Open image in new window 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 Open image in new window , 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 Open image in new window 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 parent participates too. We show that causal semantics is consistent with interaction semantics. Furthermore, it defines an isomorphism between Open image in new window and the set of the terms of Open image in new window involving triggers.

Finally, we define for causal trees a boolean representation in terms of *causal rules*.

## Keywords

Causal Chain Parallel Composition Process Algebra Interaction Scheme Causal Tree## Preview

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