By using the state equation of a Petri net, the authors derive a sufficient condition for reachability of Petri nets. Then, from this sufficient condition, they show that necessary and sufficient conditions can be derived for reachability of subclasses of a Petri net. The results presented are useful for analyzing many behavioral properties of Petri nets. >

#1Tadao Murata(UIUC: University of Illinois at Urbana–Champaign)H-Index: 23

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...

#1Ahmed Al-Ajeli(College of Information Technology)H-Index: 2

#2David Parker(University of Birmingham)H-Index: 72

Abstract null null We propose techniques for fault diagnosis in discrete-event systems modelled by labelled Petri nets, where fault events are modelled as unobservable transitions. The proposed approach combines an offline and an online algorithm. The offline algorithm constructs a diagnoser in the form of sets of inequalities that capture the legal, normal and faulty behaviour. To implement the offline algorithm, we adopt the Fourier–Motzkin method for elimination of variables from these sets o...

#1Ahmed Al-Ajeli(College of Information Technology)H-Index: 2

#2David Parker(University of Birmingham)H-Index: 72

This paper presents a new approach for the fault diagnosis problem in partially observable discrete-event systems modelled with Petri nets. Our approach is based on the use of the Integer Fourier-Motzkin Elimination (IFME) method. The fault diagnosis problem is solved by first creating an initial set of inequalities from the state equation of a Petri net. The occurrence or absence of faults can also be expressed by inequalities. After adding these inequalities to the initial set, we apply the IF...

The problem of fault diagnosis under partial observation is a complex problem; and the challenge to solve this problem is to find a compromise between the space complexity and time complexity. The classic method to solve the problem is by constructing an automaton called a diagnoser. This method suffers from the state explosion problem which limits its application to large systems. In this thesis, the problem of fault diagnosis in partially observed discrete event systems is addressed. We assume...

In this paper, the relations among T-invariants, repetitive vectors and siphons are investigated and new methods for computing repetitive vectors and siphons are suggested based on them. The transition-added net of a net is defined and a relation is shown that there always exists a T-invariant of the transition-added net corresponding to a repetitive vector of the original net, and vice versa. Based on this relation, an algorithm that can compute a set of repetitive vectors of a net is presented...

It has been known that Petri net (PN) is a useful model for analyzing discrete event systems. It is important to investigate its structural properties and behavioral properties. In this paper, first, we introduce the transformation in order to derive more useful conditions for checking structural properties and behavioral properties of an EMG. Next, we show the properties of the transformed net N' and the differences between a original net N and N'. Finally, we derive the structural properties f...

In this paper, by using the state equation of a Petri net, we derived a necessary and sufficient condition for reachability of extended marked graphs (EMGs). In particular, these conditions can be checked easily because they are presented in terms of the initial token distribution, the final token distribution, and the net structure. Furthermore, by using this necessary and sufficient condition, we can derive also the necessary and sufficient condition for a behavioral trap in EMGs.

Proposes the transformation rule in order to derive more useful condition for checking structural properties and behavioral properties of an EMG. We have shown the properties of the transformed net N' and the differences between a original net N and N'. We have also shown that the solution of its state equation had been derived by this transformation rule. Further investigation is the derivation of the necessary and sufficient condition for reachability of N and structural properties of N by usi...