Net Reachability Graph Research Articles

Robust Diagnosability Analysis Using Basis Reachability Graph

Fault-freeness is one of the necessary guarantees for healthy and stable operations of discrete event systems. Traditional diagnostic models may fail since sensors may suffer electronic component failures, communication failures, or atmospheric electromagnetic interference. Robust diagnosis problem has attracted more and more attention since it improves reliability of the diagnosis technology. When generating the Petri net reachability graph necessary for constructing a reachability diagnoser, one may face the state explosion problem. As a Petri net gets more complicated, the complexity of its reachability graph also increases exponentially. With the basis reachability graph, a lightweight diagnoser named a basis reachability diagnoser is developed, together with a robust basis reachability diagnoser obtained by dilating the basis reachability graph. Compared with reachability graphs, the advantages of basis reachability graphs in construction complexity are confirmed and the efficiency in robust diagnosability analysis is improved.

From strong to exact Petri net computers

Petri net paradigm of computing is concerned discussing basic types of Petri net computers and their relations. We developed a technique of parametric specification of Petri nets, built of a few connected components which are repeated depending on a parameter or a set of parameters, and composition of software to generate automatically the corresponding models in a vivid graphical form. We construct explicitly a Petri net that is a strong computer of double exponent after R.J. Lipton. Its nondeterministic computation is represented by a Petri net reachability graph to which a successful branch belongs. Then we minimise and transform the net to obtain twice smaller construct than the original one. Moreover, the obtained net possesses such a marvellous property that addingto it four priority arcs makes it an exact (deterministic) computer having a single firable sequence only. Same as the Lipton’s net, the minimized net allows the proof that the Petri net reachability problem is exponential in space. Besides, it represents an example when simple transformations allow guessing the successful branch of a nondeterministic computation. The practical significance of the approach in applications consists in a state-of-art heuristic technique of solving some NP problems in polynomial time.

Development of a New Strategy to Extract Dangerous Scenarios from Petrochemical Industry Installation

The use of Petri net reachability graph remains one of the most popular methods to extract critical scenarios that lead the system to a dangerous state. However, in complex systems, explosion states space and confusion between causality and precedence relationship between events are the two major limits making reachability graph inefficient to perform such analysis. In the last decade, the first limitation was tackled by an approach that uses the Petri net structure. It considers only the last normal state and ignores the rest of the network. Nevertheless, no research work appears in the literature, to consider the second limitation. In this sense, this paper proposes a novel approach based on Petri net and linear logic, to overcome the two limits. To prove the effectiveness of this proposal, the approach was applied on a petrochemical installation consisting of a cooling flammable fluids storage bins system. The obtained results are compared with the two existing approaches, the first using reachability graph and the second using the Petri net structure. The new proposed approach has shown higher performances compared to the previously mentioned methods.

Petri Nets and Deadlock-Free Scheduling of Open Shop Manufacturing Systems

In this paper, we study the open shop scheduling problem with blocking and deadlocks. First, we develop a new Petri net class that extends the well-known $\text{S}^{3}\text{R}$ nets to handle the features of open shop systems. Next, we establish necessary conditions for deadlock-free operation based on the properties of a particular structural siphon. Then, we implement a graph search algorithm that intelligently explores the net reachability graph and uses a search strategy based on a double filtering mechanism and new evaluation functions. We conducted computational tests on a set of classical instances adapted from the literature. The quality of the solutions was established with a lower bound calculated with the aforementioned siphon. The results show the validity of the approach: the proposed algorithm found solutions with values that were very close to the lower bound in most cases.

Using information flow analysis to detect implicit information leaks for web service composition

Information leak, which can undermine the compliance of web-service-composition business processes for some policies, is one of the major concerns in web service composition. We present an automated and effective approach for the detection of implicit information leaks in business process execution language (BPEL) based on information flow analysis. We introduce an adequate meta-model for BPEL representation based on a Petri net for transformation and analysis. Building on the concept of Petri net place-based noninterference, the core contribution of this paper is the application of a Petri net reachability graph to estimate Petri net interference and thereby to detect implicit information leaks in web service composition. In addition, a case study illustrates the application of the approach on a concrete workflow in BPEL notation.

ВИКОРИСТАННЯ ІНГІБІТОРНИХ МЕРЕЖ ПЕТРІ ДЛЯ ПОБУДОВИ АВТОМАТИЗОВАНОЇ СИСТЕМИ ОБЛІКУ ПАСАЖИРОПОТОКУ ГРОМАДСЬКОГО ТРАНСПОРТУ "РОЗУМНОГО" МІСТА

Визначено загальний тренд політичних ініціатив Європейського Союзу щодо модернізації та підвищення ефективності всіх сфер діяльності сучасних мегаполісів. Проведено аналіз базових принципів концепції "розумного" міста, спрямованих на оптимізацію транспортної системи сучасних міст. Доведено важливість дослідження пасажиропотоків громадського транспорту, результати якого можна використати для розроблення комплексу дій із вдосконалення організації наявних перевезень пасажирів на діючих маршрутах, а також для реорганізації транспортної мережі міста загалом. Здійснено аналіз засобів моделювання складних дискретних систем для побудови та дослідження моделей автоматизованої системи обліку пасажирів у громадському транспорті "розумного" міста. Доведено, що використання інгібіторних мереж Петрі забезпечує ефективніший процес моделювання, адже для побудови моделі на їх основі потрібно використати менше елементів мережі, що призводить до генерації чіткішого, зрозумілішого та легшого для аналізу графу досяжності станів мережі Петрі. Розроблено модель контролера збирання даних про пасажиропотік автоматизованої системи на основі інгібіторних мереж Петрі. Використання інгібіторних мереж Петрі дає змогу спростити структуру моделі, що призводить до зменшення обчислювальних ресурсів, які необхідні для реалізації моделі засобами персонального комп'ютера.

Parallel computation of the reachability graph of petri net models with semantic information

SummaryFormal verification plays a crucial role when dealing with correctness of systems. In a previous work, the authors proposed a class of models, the Unary Resource Description Framework Petri Nets (U‐RDF‐PN), which integrated Petri nets and (RDF‐based) semantic information. The work also proposed a model checking approach for the analysis of system behavioural properties that made use of the net reachability graph. Computing such a graph, specially when dealing with high‐level structures as RDF graphs, is a very expensive task that must be considered. This paper describes the development of a parallel solution for the computation of the reachability graph of U‐RDF‐PN models. Besides that, the paper presents some experimental results when the tool was deployed in cluster and cloud frameworks. The results not only show the improvement in the total time required for computing the graph, but also the high scalability of the solution, which make it very useful thanks to the current (and future) availability of cloud infrastructures. Copyright © 2016 John Wiley & Sons, Ltd.

Control Design for Trajectory Tracking With Untimed Petri Nets

This technical note is about trajectory tracking for discrete event systems. The main contribution is to compute incrementally control sequences with minimal or near-minimal length based on a partial exploration of the Petri net (PN) reachability graph and inspired by the model predictive control approach. The method is suitable for bounded and unbounded PNs, for PNs with weighted arcs and with some uncontrollable transitions. Finally forbidden markings or regions of markings are easily avoided with the proposed approach that can be used for supervisory control issues.

Persistent and Nonviolent Steps and the Design of GALS Systems

A concurrent system is persistent if throughout its operation no activity which became enabled can subsequently be prevented from being executed by any other activity. This is often a highly desirable or even necessary property; in particular, if the system is to be implemented in hardware. Over the past 40 years, persistence has been investigated and applied in practical implementations assuming that each activity is a single atomic action which can be represented, for example, by a single transition of a Petri net. In this paper we investigate the behaviour of GALS Globally Asynchronous Locally Synchronous systems in the context of VLSI circuits. The specification of a system is given in the form of a Petri net. Our aim is to re-design the system to optimise signal management, by grouping together concurrent events. Looking at the concurrent reachability graph of the given Petri net, we are interested in discovering events that appear in 'bundles', so that they all can be executed in a single clock tick. The best candidates for bundles are sets of events that appear and re-appear over and over again in the same configurations, forming 'persistent' sets of events. Persistence was considered so far only in the context of sequential semantics. In this paper, we move to the realm of step based execution and consider not only steps which are persistent and cannot be disabled by other steps, but also steps which are nonviolent and cannot disable other steps. We then introduce a formal definition of a bundle and propose an algorithm to prune the behaviour of a system, so that only bundled steps remain. The pruned reachability graph represents the behaviour of a re-engineered system, which in turn can be implemented in a new Petri net using the standard techniques of net synthesis. The proposed algorithm prunes reachability graphs of persistent and safe nets leaving bundles that represent maximally concurrent steps.

Synthesis of deadlock prevention policy using Petri nets reachability graph technique

AbstractThis paper proposes a subclass of generalized stochastic Petri net (GSPN) model, called TS3PR, which is modified the systems of simple sequential processes with resources (S3PR) with timed information. Based on the subclass of GSPN, a new deadlock prevention policy is developed by using reachability graph technique. The foundation of the new control policy is to manipulate all the dead states of the system nets. This study is able to change dead states into vanishing ones by additional immediate transitions. A live TS3PR model can then be obtained. It is worthwhile to notice that this study is different from adding additional control place policies in previous literature. Experimental results, indicate that our new control policy is with maximally permissive markings than conventional place‐control ones. As a result, we can infer that our proposed control policy seems to be used in Petri nets deadlocked systems. To our knowledge, this is the first work that employs the additional transitions to obtain the deadlock prevention policy. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Mathematical programming approach to the Petri nets reachability problem

This paper focuses on the resolution of the reachability problem in Petri nets, using the mathematical programming paradigm. The proposed approach is based on an implicit traversal of the Petri net reachability graph. This is done by constructing a unique sequence of Steps that represents exactly the total behaviour of the net. We propose several formulations based on integer and/or binary linear programming, and the corresponding sets of adjustments to the particular class of problem considered. Our models are validated on a set of benchmarks and compared with standard approaches from IA and Petri nets community.

Efficient search of Petri Nets for deadlock-free scheduling in FMSs using heuristic functions

This paper presents and evaluates the performance of three heuristic functions, based on Petri Nets (PN), which are used to optimize the average flow time in flexible manufacturing systems. The developed heuristic functions aim to reduce the complexity of the scheduling problem by searching only the necessary portion of the Petri Net reachability graph. In addition, each heuristic function is equipped with a parameter to provide a trade-off between the solution quality and the search effort. A major advantage of these heuristics is in the case of modification to deal with other measures of performance such as resources utilization and due date measures. An experimental study was performed using these heuristic functions on randomly generated test cases. A new routine for automatically generating PN models from a production plan is presented. The Average Operation Waiting Time (AOWT) heuristics function is found to outperform the other two functions, Remaining Processing Time (RPT) and Scheduling with Dispatching Rules (SDR), with respect to the obtained average flow time and the solution CPU time. In addition, the newly developed heuristics help in scheduling larger problems with high efficiency compared with the results reported in the literature.

Liveness-enforcing supervision of bounded ordinary Petri nets using partial order methods

This paper combines and refines recent results into a systematic way to verify and enforce the liveness of bounded ordinary Petri nets. The approach we propose is based on a partial-order method called network unfolding. Network unfolding maps the original Petri net to an acyclic occurrence net. A finite prefix of the occurrence net is defined to give a compact representation of the original net reachability graph while preserving the causality between net transitions. A set of transition invariants denoted as base configurations is identified in the finite prefix. These base configurations capture all of the fundamental executions of the net system, thereby providing a modular way to verify and synthesize supervisory net systems. This paper proves necessary and sufficient conditions that characterize the original net liveness and the existence of maximally permissive supervisory policies that enforce liveness.

Petri nets with generalized algebra: a comparison

In the last decade we can see substantial effort to develop an abstract and uniform constructions for Petri nets. Most of such abstractions are based on algebraic characterizations of Petri nets. They work mostly over commutative monoids and their various subclasses, namely cancellative commutative monoids or cones of Abelian groups. In the paper we study relationships between Petri nets with generalized underlying algebra. More precisely, we study Petri nets over commutative monoids, cancellative commutative monoids, cones of Abelian groups, and fully ordered cones of Abelian groups. As the main result, we show that classes of reachability graphs of Petri nets over cancellative commutative monoids and cones of Abelian groups coincide (up to isomorphism). In other words, partial order on used cancellative commutative monoid plays no role in expressive power of Petri nets. However, as shows the fact that the class of reachability graphs of nets over fully ordered cones is a proper subclass of the class of reachability graphs of nets over cancellative commutative monoids, the total order on used monoids plays an important role in expressive power of Petri nets.