Connector algebras for C/E and P/T nets' interactions

A quite flourishing research thread in the recent literature on component-based systems is concerned with the algebraic properties of different classes of connectors.In a recent paper, an algebra of stateless connectors was presented that consists of fivekinds of basic connectors, namely symmetry, synchronization, mutual exclusion, hidingand inaction, plus their duals, and it was shown how they can be freely composed in seriesand in parallel to model sophisticated “glues”. In this paper we explore the expressivenessof stateful connectors obtained by adding one-place buffers or unbounded buffers to thestateless connectors. The main results are: i) we show how different classes of connectorsexactly correspond to suitable classes of Petri nets equipped with compositional interfaces,called nets with boundaries; ii) we show that the difference between strong and weaksemantics in stateful connectors is reflected in the semantics of nets with boundaries bymoving from the classic step semantics (strong case) to a novel banking semantics (weakcase), where a step can be executed by taking some “debit” tokens to be given back duringthe same step; iii) we show that the corresponding bisimilarities are congruences (w.r.t.composition of connectors in series and in parallel); iv) we show that suitable monoidalitylaws, like those arising when representing stateful connectors in the tile model, can nicelycapture concurrency (in the sense of step semantics) aspects; and v) as a side result, weprovide a basic algebra, with a finite set of symbols, out of which we can compose all P/Tnets with boundaries, fulfilling a long standing quest. 1998 ACM Subject Classification: F.1.1; F.4.3.