Compositional semantics for open Petri nets based on deterministic processes

Abstract

In order to model the behaviour of open concurrent systems by means of Petri nets, we introduce open Petri nets, a generalisation of the ordinary model where some places, designated as open, represent an interface between the system and the environment. Besides generalising the token game to reflect this extension, we define a truly concurrent semantics for open nets by extending the Goltz-Reisig process semantics of Petri nets. We introduce a composition operation over open nets, characterised as a pushout in the corresponding category, suitable for modelling both interaction through open places and synchronisation of transitions. The deterministic process semantics is shown to be compositional with respect to such a composition operation. If a net Z 3 results as the composition of two nets Z 1 and Z 2 , having a common subnet Z 0 , then any two deterministic processes of Z 1 and Z 2 that 'agree' on the common part, can be 'amalgamated' to produce a deterministic process of Z 3. Conversely, any deterministic process of Z 3 can be decomposed into processes of the component nets. The amalgamation and decomposition operations are shown to be inverse to each other, leading to a bijective correspondence between the deterministic processes of Z 3 and the pair of deterministic processes of Z 1 and Z 2 that agree on the common subnet Z 0. Technically, our result is similar to the amalgamation theorem for data-types in the framework of algebraic specification. A possible application field of the proposed constructions and results is the modelling of interorganisational workflows, recently studied in the literature. This is illustrated by a running example. † This research was partially supported by the EC TMR Network GETGRATS (General Theory of Graph Transformation Systems), by the ESPRIT Working Group APPLIGRAPH (Applications of Graph Transformation), and by the MURST project TOSCA (Teoria della Concorrenza, Linguaggi di Ordine Superiore e Strutture di Tipi).

Encoding Asynchronous Interactions Using Open Petri Nets

“…This section reviews open nets, i.e., ordinary P/T nets with a distinguished set of open places: they represent the interfaces through which the environment interacts with a net, by putting and removing tokens (see [21][22][23]). …”

“…We propose an approach to process encoding which differs from those outlined above, as it relies on reduction semantics [19,20] and open nets [21][22][23]. Open nets are ordinary P/T Petri nets equipped with a set of open places, i.e., a set of places visible from the environment: a net may then interact with the environment by exchanging tokens on these places.…”

Reconfiguring Distributed Reo Connectors

“…Modeling the distribution of systems via embedding interfaces represented as morphisms in a suitable category is also used for open Petrinets [9]. The explicit modeling of glue code and the exploitation of pushout constructions to deal with composition in this work is similar to ours.…”

“…However, they do not consider the application of double pushouts and their concept of amalgamation is different. In [9], amalgamation serves the composition of deterministic processes of open Petri-nets, whereas in our approach it is used as a synchronization mechanism for the superposition of local reconfiguration rules.…”

Open Petri Nets: Non-deterministic Processes and Compositionality

“…In particular, open Petri nets, as introduced in [1], are a mild extension of basic nets with the possibility of interacting with the environment and of composing a larger net out of smaller open components. An open net is an ordinary net with a distinguished set of places, designated as open, through which the net can interact with the environment.…”