High-level Petri nets as type theories in the join calculus

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, IIi, introduce a hierarchy of type systems of decreasing strictness, Δi, i = 0,…3, and we prove that a join process is typeable according to Δi if and only if it is (strictly equivalent to) a net of class IIi. In the details, II0 and II1 contain, resp., usual place/transition and coloured Petri nets, while II2 and II3 propose two natural notions of high-level net accounting for dynamic reconfiguration and process creation and called reconfigurable and dynamic Petri nets, respectively.