Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >

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Petri nets: Properties, analysis and applications

A fundamental difficulty in automatic formal verification of finite-state systems is thestate explosion problem—even relatively simple systems can produce very large state spaces, causing great difficulties for methods that rely on explicit state enumeration. We address the problem by exploiting structuralsymmetries in the description of the system to be verified.

Better Verification Through Symmetry

Coloured Petri nets (CPN) is a formalism which extends ordinary Petri nets by adding data types and modularity. This means that is possible to make succinct, readable and structured models. The CPN models may be investigated by means of simulation. However, the models may also be validated by a number of mathematical analysis techniques, such as state graphs and invariants. The modelling, simulation and analysis by means of CPN are supported by a set of commercially available computer tools called Design/CPN. CPN models have been used in a large range of different application areas, some of which are listed. Design/CPN uses the functional programming language Standard ML to specify data types, functions and data manipulations. 12 properties of CPN are presented. >

https://ieeexplore.ieee.org/iel3/1386/6485/00255880.pdf

Coloured Petri nets

This paper describes how Coloured Petri Nets (CP-nets) have been developed — from being a promising theoretical model to being a full-fledged language for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and/or computers communicate by means of some more or less formal rules).

Coloured Petri Nets: a high level language for system design and analysis

This paper describes a Petri net model, called Coloured Petri nets (CP-nets), where information is attached to each token. The information can be inspected and modified when a transition fires. For most applications, this generalization of ordinary Petri nets allows the user to make more manageable descriptions, due to the fact that equal subnets can be folded into each other, yielding a much smaller net. The paper investigates how to analyse Coloured Petri nets. It turns out that place-invariants and reachability trees, two of the most important methods for ordinary Petri nets, can be generalized to apply for Coloured Petri nets.

Coloured Petri Nets

High-level Petri nets have been introduced as a powerful net type, by which it is possible to handle rather complex systems in a succinct and manageable way. The success of high-level Petri nets is undebatable when we speak about description, but there is still much work to be done to establish the necessary analysis methods. It has already been shown how to generalize the concept of place-invariants and transition-invariants, from place-transition-nets to high-level Petri nets. Our present paper constitutes the first steps towards a generalization of reachability trees, which is one of the other important analysis methods known for PT-nets. The central idea in our paper is the observation, that HL-nets often possess classes of equivalent markings. As an example an HL-net describing the five dining philo\-sophers has an equivalence-class consisting of those five markings in which exactly one philosopher is eating. These five markings are interchangeable, in the sense that their subtrees represent equivalent behaviours, where the only difference is the identity of the involved philosophers and forks. If we analyze one of these subtrees, we also understand the behaviour of the others. We describe an algorithm which constructs the HL-tree. The algorithm can easily be automated and we will soon start the work on an implementation. The constructed HL-trees turn out to be considerably smaller than the corresponding PT-trees (reachability trees for the equivalent PT-nets).

Leif O. Jepsen

Papers

Towards reachability trees for high-level Petri nets

Reachability trees for high-level petri nets

Towards Reachability Trees for High-level Petri Nets