High-Level Petri Nets as Type Theories in the Join Calculus

Abstract

Abstract. We study the expressiveness of the join calculus by comparison with (generalised, coloured) Petri nets and using tools from type theory. More precisely, we consider four classes of nets of increasing expressiveness, Π i, introduce a hierarchy of type systems of decreasing strictness, ∆i, i = 0, . . . , 3, and we prove that a join process is typeable according to ∆i if and only if it is (strictly equivalent to) a net of class Πi. In the details, Π0 and Π1 contain, resp., usual place/transition and coloured Petri nets, while Π2 and Π3 propose two natural notions of high-level net accounting for dynamic reconfiguration and process creation and called reconfigurable and dynamic Petri nets, respectively.

Petri net-based process monitoring: a workflow management system for process modelling and monitoring

“…On the one hand, Petri nets can be used as a design language for the specification of complex workflows; on the other hand, Petri net theory and notation provides powerful techniques for workflow analysis. Moreover, Petri nets can be extended to high level Petri nets [13] which allows a more accurate representation of the workflow representation. For example, Eshuis et al [15] pointed that a limitation of Petri nets is that a transition does not necessarily fires at the time instant when a task is carried, it can be fired at an aleatory time after the execution.…”

Encoding Asynchronous Interactions Using Open Petri Nets

“…Indeed, even if our presentation has been tailored over a variant of standard CCS, we feel confident that it can be generalized to other asynchronous calculi as well, at least to those based on a primitive notion of communication, i.e., without either value or name passing. As suggested by the work in [15,30,32], the generalisation to calculi with value or name passing looks feasible if one considers more expressive variants of Petri nets, ranging from high-level to reconfigurable/dynamic Petri nets.…”

“…We consider such a correspondence quite enlightening, since most of the encodings we are aware of focus on the preservation of some variants of reachability or of the operational behaviour [30][31][32]40], while ours allow to establish a correspondence at the observational level.…”

“…This is e.g. the pattern followed in [30], which considers possible encodings of the join calculus, where communication is asynchronous, into Petri nets. In particular, the fragment of the join calculus with no name passing and process generation is shown to correspond to ordinary P/T Petri nets, while, in order to encode wider classes of join processes, high-level Petri nets, ranging from coloured nets to dynamic nets must be considered.…”

“…Some related work has been done in the direction of encoding several brands of coordination languages, where processes communicate through shared dataspaces, as Petri nets. The papers [30,31] exploit the encoding to compare the expressiveness of Linda-like calculi with various communication primitives. In [32] an encoding of KLAIM, a Linda-like language with primitives for mobile computing, into high-level Petri nets is provided.…”