Dynamic Modification of System Structures Using LLPNs

In this paper we aim to set up a framework for object Petri net semantics, allowing the modification of object net structures at runtime. The approach uses linear logic Petri nets (LLPNs) and performs the structure modification on a linear logic encoding of the object net. In addition, Valk’s self-modifying Petri nets are shown to be subsumed by LLPNs. We expand on the existing theory of Farwer’s LLPNs, which are Petri nets with linear logic formulae as tokens. This work in progress uses intuitionistic linear logic as the basis of a method for ensuring desirable properties—such as termination or non-termination—of P/T nets, coloured Petri nets and LLPNs. 1 Background and Motivation Petri nets are well-known models for concurrent and reactive systems. A placetransition net (P/T net) is a type of Petri net with places which can contain tokens and transitions that are connected by directed, weighted arcs. Diagramatically, places are represented by circles and transitions by rectangles. The precondition of a transition is the number of tokens needed in each place for the transition to be enabled, and is indicated by the weights of the incoming arcs. The postcondition of a transition is the number of tokens generated in each place by the firing of the transition, and is indicated by the weights of the outgoing arcs. A transition fires when its precondition is satisfied, after which its postcondition is generated. This is shown in Figure 1. P/T nets have been extended in several ways. Coloured Petri nets (CPNs) were introduced under the name of “high-level Petri nets” by Jensen [16]. CPNs 2 transition place1 place2 3 2 transition place1 place2 3 transition