A formal algebraic approach for the quantitative modeling of connectors in architectures

TL;DR

This paper introduces an algebraic formalization for modeling the non-functional features of connectors in component-based system architectures, extending existing models to include weighted coordination schemes.

Contribution

It develops a weighted algebraic framework for connectors, incorporating synchronization types and congruence relations, advancing formal modeling of system architectures.

Findings

Modeling of weighted connectors for various coordination schemes

Introduction of subalgebras for synchronization and triggers

Conditions for congruence relations in weighted connectors

Abstract

In this paper we propose an algebraic formalization of connectors in the quantitative setting, in order to address their non-functional features in architectures of component-based systems. We firstly present a weighted Algebra of Interactions over a set of ports and a commutative and idempotent semiring, which is proved sufficient for modeling well-known coordination schemes in the weighted setup. In turn, we study a weighted Algebra of Connectors over a set of ports and a commutative and idempotent semiring, which extends the weighted Algebra of Interactions with types that encode Rendezvous and Broadcast synchronization. We show the expressiveness of the algebra by modeling the weighted connectors of several coordination schemes. Moreover, we derive two subalgebras, namely the weighted Algebra of Synchrons and the weighted Algebra of Triggers, and study their properties. Finally, we introduce a concept of congruence relation for connectors in the weighted setup and we provide conditions for proving such a congruence.