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A quite flourishing research thread in the recent literature oncomponent-based systems is concerned with the algebraic properties of differentclasses of connectors. In a recent paper, an algebra of stateless connectorswas presented that consists of five kinds of basic connectors, namely symmetry,synchronization, mutual exclusion, hiding and inaction, plus their duals, andit was shown how they can be freely composed in series and in parallel to modelsophisticated 'glues'. In this paper we explore the expressiveness of statefulconnectors obtained by adding one-place buffers or unbounded buffers to thestateless connectors. The main results are: i) we show how different classes ofconnectors exactly correspond to suitable classes of Petri nets equipped withcompositional interfaces, called nets with boundaries; ii) we show that thedifference between strong and weak semantics in stateful connectors isreflected in the semantics of nets with boundaries by moving from the classicstep semantics (strong case) to a novel banking semantics (weak case), where astep can be executed by taking some 'debit' tokens to be given back during thesame step; iii) we show that the corresponding bisimilarities are congruences(w.r.t. composition of connectors in series and in parallel); iv) we show thatsuitable monoidality laws, like those arising when representing statefulconnectors in the tile model, can nicely capture concurrency (in the sense ofstep semantics) aspects; and v) as a side result, we provide a basic algebra,with a finite set of symbols, out of which we can compose all P/T nets withboundaries, fulfilling a long standing quest.

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