Event Structures for Local Traces

International audience

The PETRI NETS 2023 proceedings deal with the application and theory of petri nets, distributed and concurrency systems, etc.

The intention of this note is to spread the Couvreur et al.’s semantic framework of branching processes [9], suitable for describing the behavior of general Petri nets with interleaving semantics, to timed general Petri nets with step semantics in order to characterize unfolding as the greatest element of a complete lattice of branching processes. In case of maximal step semantics of timed Petri nets, we impose some restrictions on the model behavior and define a new class of branching processes and unfoldings under the name of apt ones which are shown to satisfy the complete lattice properties.

A Petri net can provide a graphical model of a concurrent system. They have been used to model such varied systems as resource control, communication networks and manufacturing processes. Computer Science students will, hopefully, learn the theory of Petri nets in a discrete mathematics course or a course on theoretical foundations of Computer Science. They may even see a graph of a sample net in a textbook, but it is unlikely they will have a chance to experiment with a live net. The Interactive Petri Net Simulator (IPNetS) described in this paper provides an easy point-and-click environment for students to design, modify, examine, and execute a Petri net. In seconds any simple Petri net can be created and animated. IPNetS provides display, file handling, and user control functions while a separate execution unit does the actual execution of the net. This flexible design allows for easy experimentation with different execution units and different types of nets. An Ada and a C++ execution unit are contrasted.

To simulate and debug or diagnose manufacturing systems is always challenging. This paper presents a hybrid PLC-controlled and PC Visual Basic (VB)-based Human-Machine Interface (HMI) platform based on Petri net (PN) theory for Manufacturing Systems. An augmented PN model was adopted to design and simulate the operational sequence of the Flexible Manufacturing System (FMS) at the National Kaohsiung First University of Science and Technology (NKFUST). With the simulated PN model, the control sequences were quickly translated into PLC programs. A PC-based HMI monitoring system based on the PN model was developed to provide an intuitive offline simulation and online diagnostic tools for the FMS. This hybrid system shows many of advantages by using the economical discrete control unit with PLC, and PC-based HMI using PN model as a base. The discrete event control sequence of an FMS can be easily modeled and evaluated before its build-up. More importantly, it can be diagnosed online when the system is malfunctioning. That is, the presented system provides an adequate means for offline system design, simulation, performance evaluation, and quick online system diagnostic.

A Survey of Reachability Trees of Unbounded Petri Nets

Hemojuvelin–hepcidin axis modeled and analyzed using Petri nets

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of history-preserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has ``refinement'' operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising Hennessy-Milner logic, which is characteristic for the generalised notion of bisimulation.

We review the conceptual development of (true) concurrency and branching time starting from Petri nets and proceeding via Mazurkiewicz traces, pomsets, bisimulation, and event structures up to higher dimensional automata (HDAs), whose acyclic case may be identified with triadic event structures and triadic Chu spaces. Acyclic HDAs may be understood as extending the two truth values of Boolean logic with a third value .

This paper develops a novel hybrid intelligent method, which is combined Petri Net (PN) model with Ant Colony Optimization (ACO) to solve target network reconfiguration strategy for power system restoration. The target network is firstly modeled by Petri Net (PN) theory. In order to find the shortest restored energized path effectively, the transition rules of PN and the ACO algorithm are integrated elaborately. Finally, the case studies for IEEE 30-bus system as benchmark are applied to demonstrate the validity and effectiveness of the proposed model and method. (4 pages)

Hybrid continuous-time and discrete-event system models are developed for applications to intelligent robot and autonomous control systems. Certain general properties, including the interface structure between the discrete event part and the continuous part of hybrid systems, are studied. Petri nets are proposed as the model for the discrete event sub-system (DES), and state equations with a set of binary parameters as the model for the continuous time sub-system (CTS) in a hybrid system. The quantized CTS is formulated in prime event structures, which can also be modeled by a condition/event Petri net. Therefore, a complete hybrid system can be fit into an extended Petri net formalism, which provides a unified framework for hybrid system description. The validity of the proposed model is demonstrated by modeling a two-tank system.

Event structures and trace monoids

The construction and analysis of OR-problems are considered under the assumption that the problem structures depend essentially on logical constituents. The conventional approach to use binary (“0/1”) variables suffers from models which are very complicated and intransparent. The nature of logical constitutents is not “adequately” represented by complexes of binary variables. As an alternative the net-theoretic approach can be used to construct graphical problem descriptions. These descriptions base on the propositional or predicate logic and the theory of Petri nets. The resulting net models have the advantages of compactness and easy interpretation. Furthermore conventional arithmetic and logically based algorithrns can be applied to the analysis of net models (for consistency checks e.g.). The efficiency of model construction and analysis is not considered. Instead of this the preceding aspect is explored which contributions to problem modelling result from combining logic, net theory, linear arithmetic and graphical problem description. An example demonstrates these results. It concerns the design of annual balance sheets of stock corporations with regard to corporate income tax.

It is very difficult for ECA rules system to be analyzed and validated. And there is no perfect model which can be used today. This paper, on basis of Petri net theory, makes modeling research on ECA rules, establishes basic Petri net model; meanwhile makes special research that how to use Petri net express compound event ECA rules; put forward extended Petri net system, and considers its feature of ECA rules in general, reflects system feature of ECA rules in all aspects. Through forming reachability tree and transition sequence, it can understand ECA rules system and its action feature clearly, is convenient to make rationality verification on rules system, so as to help system administrator to make analysis and management on it. As a matter of course, this paper makes analysis on simple system action of ECA rules, it still need further research how to use Petri net technology to make analysis on system action of rules, like terminability and parallelism.

In this chapter, modeling of GRNs using Petri net theory is considered. It aims at providing a conceptual understanding of Petri nets to enable the reader to explore GRNs applying Petri net modeling and analysis techniques. Starting with an overview on modeling biochemical networks using Petri nets, the state-of-the-art with focus on GRNs is described. Other modeling techniques, for example, hybrid Petri nets are discussed. Basic concepts of Petri net theory are introduced involving special analysis techniques for modeling biochemical systems, for example, MCT-sets, T-clusters, and Mauritius maps. To illustrate these Petri net concepts, a more complex case study–the gene regulation in Duchenne Muscular Dystrophy–is explained in detail, considering the biological background and the interpretation of analysis results. Considering both, advantages and disadvantages, the chapter demonstrates the usefulness of Petri net modeling, in particular for GRNs.