Class Of Petri Nets Research Articles

On the Complexity of Proving Polyhedral Reductions

We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer constraints between the marking of places. In addition to defining an automated proof method, this paper aims to better characterize polyhedral reductions, and to give an overview of their application to reachability problems. Our approach relies on encoding the equivalence problem into a set of SMT formulas whose satisfaction implies that the equivalence holds. The difficulty, in this context, arises from the fact that we need to handle infinite-state systems. For completeness, we exploit a connection with a class of Petri nets, called flat nets, that have Presburger-definable reachability sets. We have implemented our procedure, and we illustrate its use on several examples.

Taking Complete Finite Prefixes To High Level, Symbolically*

Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of a P/T Petri net’s unfolding contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. We evaluate this extended algorithm through a prototype implementation on four novel benchmark families. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.

Event-Based Modeling of Input Signal Behaviors for Discrete-Event Controllers

Controllers for discrete-event systems are commonly designed using state-based formalisms, like state diagrams and Petri nets. These formalisms are strongly supported by the concept of events, which, from an automation system perspective, can be associated with a simple change in the value of a signal or more complex behavioral evolutions of the signals. In this paper, the characterization of several types of events is proposed, associated with different types of signals, such as Boolean and multivalued signals. The major goal of this characterization is to improve the compactness of the model, benefiting the editing and visual interpretation of the graphical model but keeping precise execution semantics, which in turn allows for the use of computational tools covering the different stages of system development. The behavioral model of the controller is produced using a non-autonomous class of Petri nets, the IOPT nets, and the associated IOPT-Tools, which supports the specification, simulation, property verification, and automatic code generation ready to be deployed into implementation platforms. All the types of proposed events have a behavioral sub-model executed concurrently with the main model of the controller. An application example is provided to illustrate some of the advantages of the adoption of the proposed approach, encapsulating the behavioral dependencies on the evolution of input signals into events.

Verification of Unary Communicating Datalog Programs

We study verification of reachability properties over Communicating Datalog Programs (CDPs), which are networks of relational nodes connected through unordered channels and running Datalog-like computations. Each node manipulates a local state database (DB), depending on incoming messages and additional input DBs from external services. Decidability of verification for CDPs has so far been established only under boundedness assumptions on the state and channel sizes, showing at the same time undecidability of reachability for unbounded states with only two unary relations or unbounded channels with a single binary relation. The goal of this paper is to study the open case of CDPs with bounded states and unbounded channels, under the assumption that channels carry unary relations only. We discuss the significance of the resulting model and prove the decidability of verification of variants of reachability, captured in fragments of first-order CTL. We do so through a novel reduction to coverability problems in a class of high-level Petri Nets that manipulate unordered data identifiers. We study the tightness of our results, showing that minor generalizations of the considered reachability properties yield undecidability of verification, both for CDPs and the corresponding Petri Net model.

Supervisor Synthesis for Petri Nets With Uncontrollable and Unobservable Transitions

This paper focuses on designing event feedback supervisors to enforce control specifications on Petri nets with uncontrollable and unobservable transitions. For each observation, the supervisor is able to select some controllable transitions to disable such that the system never reaches illegal markings. Two different methods are given to design such a supervisor. The first method computes the control policy by solving some integer linear programming problems, while the second one designs supervisors by taking advantage of the structural properties of a class of Petri nets. The computational efficiencies of these two methods increase successively at the expense of their application scopes. Two examples are given to illustrate the proposed methods, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper consists in ensuring the behavior of a manufacturing system within a given legal behavior. The typical task for a designer is to design a supervisor to restrict that the system never reaches a forbidden state under limited control and observation ability. To this end, this paper proposes two different methods to design such a supervisor. The first one needs to solve integer linear programming problems, while the second one is based on the structural analysis of a special class of systems. It should be noted that although the application scope of the first method is wider, the second method has higher computational efficiency. Therefore, the suitable method can be chosen in accordance with the specific application scenario, which is significant and useful to manufacturing engineers.

Adaptive supervisory control for a class of Petri nets with bimodal transitions

Adaptive supervisory control for a class of Petri nets with bimodal transitions

Searching for significant reactions and subprocesses in models of biological systems based on Petri nets

The primary aim of this research was to propose algorithms enabling the identification of significant reactions and subprocesses within models of biological systems constructed using classical Petri nets. These solutions allow to performance of two analysis methods: an importance analysis for identifying individual reactions critical to the functioning of the model and an occurrence analysis for finding essential subprocesses. To demonstrate the utility of these methods, analyses of an example model have been performed. In this case, it was a model related to the DNA damage response mechanism. It is worth noting that the proposed analyses can be applied to any biological phenomenon represented using the Petri net formalism. The presented analysis methods represent an extension of classical Petri net-based analyses. Their utility lies in their potential to enhance our comprehension of the biological phenomena under investigation. Furthermore, they can lead to the development of more effective medical therapies, as they can aid in the identification of potential molecular targets for drugs.

ProcessChain: a blockchain-based framework for privacy preserving cross-organizational business process mining from distributed event logs

PurposeThe purpose of this paper is to design a consortium-blockchain based framework for cross-organizational business process mining complying with privacy requirements.Design/methodology/approachBusiness process modeling in a cross-organizational setting is complicated due to privacy concerns. The process mining in this situation occurs through trusted third parties (TTPs). It uses a special class of Petri-nets called workflow nets (WF-nets) to represent the formal specifications of event logs in a blockchain-enabled cross-organization.FindingsUsing a smart contract algorithm, the proposed framework discovers the organization-specific business process models (BPM) without a TTP. The discovered BPMs are formally represented using WF-nets with a message factor to support the authors’ claim. Finally, the applicability and suitability of the proposed framework is demonstrated using a case study of multimodal transportation.Originality/valueThe proposed framework complies with privacy requirements. It shows how to represent the formal specifications of event logs in a blockchain using a special class of Petri-nets called WF-nets. It also presents a smart contract algorithm to discover organization-specific business process models (BPM) without a TTP.

On the Complexity of Techniques That Make Transition Systems Implementable by Boolean Nets

Let us consider some class of (Petri) nets. The corresponding Synthesis problem consists in deciding whether a given labeled transition system (TS) A can be implemented by a net N of that class. In case of a negative decision, it may be possible to convert A into an implementable TS B by applying various modification techniques, like relabeling edges that previously had the same label, suppressing edges/states/events, etc. It may however be useful to limit the number of such modifications to stay close to the original problem, or optimize the technique. In this paper, we show that most of the corresponding problems are NP-complete if the considered class corresponds to so-called flip-flop nets or some flip-flop net derivatives.

Automated modelling of discrete-event processes. Discovering Petri nets including silent transitions by classifying event traces

ABSTRACT This paper addresses the problem of automated modelling of discrete-event processes from event traces that capture the process behaviour. A novel method for building Petri nets (PN) that include silent transitions is presented. The method discovers workflow nets (WFN), a class of PN, from logs of event traces λ. The proposed approach is based on a classification of traces such that λ is partitioned into four classes: normal traces (λN), which do not involve the firing of silent transitions; skip traces (λS), redo traces (λR), and switch traces (λSW), which involve the firing of skip, redo, and switch type silent transitions, respectively. Afterwards, traces in λN are used to build a base WFN N, which may include silent transitions of type initialise and finalise. Then, N is refined by adding the silent transitions corresponding to the classes oftraces λS, λR, and λSW. The algorithms of the method have polynomial-time complexity; implementation and tests using artificial event logs are presented.

Array generating fuzzy petri nets and rectangular picture languages

A two dimensional language is a collection of two dimensional words, which are rectangular array of symbols made up of finite alphabets. Fuzzy Petri nets are the generalization of classical Petri nets designed to deal with imprecise and ambiguous data which usually occurs in knowledge based systems, image processing, etc. They have been widely used to represent fuzzy production rules and fuzzy rule-based reasoning. In this paper, a new model called array token fuzzy Petri net to generate two dimensional fuzzy regular languages has been introduced. Array token fuzzy Petri nets are used to deal with impreciseness and uncertainties occurring in two dimensional regular languages. Furthermore, proved that for every two dimensional fuzzy regular grammar there exists an array token fuzzy Petri net that generates the same two dimensional fuzzy regular language and also establish some closure properties of the languages generated by array token fuzzy Petri net.

Cross-Department Collaborative Healthcare Process Model Discovery From Event Logs

Healthcare plays an increasingly essential role in our daily life. Modern Hospital Information Systems (HISs) record and store detailed medical treatment process information for all patients as event logs. By taking event logs as input, process mining techniques have been widely applied to extract valuable insights to improve medical treatment processes and deliver better healthcare services. However, considering the complexity of collaborations among different medical departments, existing model discovery techniques cannot be applied directly. To handle this limitation, this paper proposes a novel approach to support the discovery of Cross-department Collaborative Healthcare Process (CCHP) models from medical event logs. Specifically, an extension of classical Petri Nets with message and resource attributes is first introduced to formalize CCHPs. Then, a novel discovery algorithm is proposed to discover Intra-department Healthcare Process (IHP) models. Next, collaboration patterns among medical departments are formalized and corresponding discovery algorithms are given on that basis. Finally, a global CCHP model is obtained by integrating all discovered collaboration patterns and IHP models. By using four public medical event logs, we quantitatively compare our approach with the state-of-the-art process mining techniques in terms of model quality, and our experimental results demonstrate that the proposed approach can discover more accurate healthcare process models. <i>Note to Practitioners</i>&#x2014;The recorded medical event logs by HISs can be used to extract valuable insights for the analysis of healthcare processes. However, existing process model discovery techniques cannot be applied for the analysis directly due to the complex collaborations among different medical departments of a hospital. This paper introduces a novel approach for cross-department collaborative healthcare process model discovery from medical event logs. All proposed techniques are fully implemented and publicly available. Using four public medical event logs, we show the applicability and advantages of our approach against existing ones. The proposed techniques are applicable to the model discovery and behavior understanding of real-life operational healthcare processes.

On Liveness Enforcement of Distributed Petri Net Systems

In this paper, we consider the liveness enforcement problem in a class of Petri nets (PN) modeling distributed systems. They are called <i>synchronized sequential processes</i> (SSP). The presented design algorithm is based on the construction of a control PN, an abstraction of the relations of the T-semiflows, and buffers of the original nonstructurally live PN. The <i>control PN</i> evolves in parallel with the system, avoiding the firing of transitions that may lead the system to non liveness. Four algorithms are presented, one allowing for the computation of the control PN and three ensuring its liveness.

Soundness-preserving composition of synchronously and asynchronously interacting workflow net components

In this paper, we propose a compositional approach to constructing correct formal models of information systems from correct models of interacting components. Component behavior is represented using workflow nets — a class of Petri nets. Interactions among components are encoded in an additional interface net. The proposed approach is used to model and compose synchronously and asynchronously interacting workflow nets. Using Petri net morphisms and their properties, we prove that the composition of interacting workflow nets preserves the correctness of components and of an interface.

Small-Size Liveness-Enforcing Supervisor for Automated Manufacturing Systems Using the Theory of Transition Cover

The supervisor simplification problem for automated manufacturing systems (AMSs) has been receiving increasing attention in recent years. This article uses a well-known class of Petri nets, namely, systems of sequential systems with shared resources (S4Rs) to model general AMSs. We aim to simplify the liveness-enforcing supervisor for S4R by using the concept of transition cover (TC). Deadlocks in S4R can be characterized by a kind of special structural object called perfect activity circuits (PACs). First, a set of special PACs are defined as a TC and its effectness is also verified. Then, by adding a monitor with a control variable to each PAC in an effective TC (ETC), we establish a liveness-enforcing supervisor for S4R. The control variables are determined by solving an integer linear programming problem so as to increase the supervisor’s permissiveness as much as possible. Under the proposed control methodology, it is analyzed that the upper bound of the number of monitors equates to that of transitions in S4R. Especially for the system with a few transitions, since not many monitors are added, the proposed supervisor has relatively small-scaled structures or a small number of control places. In addition, we present algorithms to get an ETC from any nonlive S4R. Based on this ETC, we can design one liveness-enforcing supervisor of small size for the underlying S4R. Finally, some examples are used to illustrate the proposed approach.

Robust Petri Net Controllers for Flexible Manufacturing Systems With Multitype and Multiunit Unreliable Resources

It is inevitable that resource failures occur in real production processes, and sometimes many different types of unreliable resource failures may occur. Once there are resource failures, the stagnation states of production caused by these failures, called as failure blockings (FBs), tend to appear. Hence, both deadlocks and FBs can arise to reduce production efficiency sharply. Designing robust control policies for such an automated system is thus very important. Our work focuses on a novel robust Petri net controller of flexible manufacturing systems with multitype and multiunit of unreliable resources. First, under the assumption that all resources are reliable, these systems are modeled by a class of Petri nets called systems of simple sequential processes with resources (S3PRs). For each operation place that is a holder of an unreliable resource, the corresponding repair place and related transitions are added to the net and an S3PR with unreliable resources (S3PRu) is developed. For an S3PRu, the formal definition of FBs is then proposed. Such an FB is characterized by a maximal perfect resource-transition circuit (MPC). Next, the concept of a critical set of MPCs is introduced. For any two adjacent MPCs in such a critical set, one input transition of the former and one output transition of the latter are connected by passing through resource places. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resource is a one-unit resource shared by two or more MPCs that do not contain each other. For an S3PRu without <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resources and critical sets of MPCs, a control place corresponding to an MPC is added to the net with its output arcs to the input transitions of the MPC. However, for an S3PRu with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\xi $ </tex-math></inline-formula> -resources or critical sets of MPCs, the output arcs of each control place are added to the source transitions of the original net. Thus, a novel robust controller of an S3PRu is synthesized. Such a robust controller can guarantee that as long as at least one unit of each type of unreliable resources can work normally, all kinds of parts can be processed to complete smoothly their tasks through any one of their process routes. Finally, three examples are provided to illustrate the efficiency of the proposed robust controller.

Performance Optimization for a Class of Petri Nets.

Petri nets (PNs) are widely used to model flexible manufacturing systems (FMSs). This paper deals with the performance optimization of FMSs modeled by Petri nets that aim to maximize the system's performance under a given budget by optimizing both quantities and types of resources, such as sensors and devices. Such an optimization problem is challenging since it is nonlinear; hence, a globally optimal solution is hard to achieve. Here, we developed a genetic algorithm combined with mixed-integer linear programming (MILP) to solve the problem. In this approach, a set of candidate resource allocation strategies, i.e., the choices of the number of resources, are first generated by using MILP. Then, the choices of the type and the cycle time of the resources are evaluated by MILP; the promising ones are used to spawn the next generation of candidate strategies. The effectiveness and efficiency of the developed methodology are illustrated by simulation studies.

Graphic Model for Shop Floor Simulation and Control in the Context of Industry 5.0

Industry 5.0 changes the paradigm of the current production model, with repercussions throughout the value chain, and opens up opportunities for new approaches that include reducing waste to optimize the use of the planet’s resources. This paper proposes a functional and executable model that implements a Holonic Manufacturing System (HMS) architecture inspired by the I5.0 guidelines. This architecture presents the factory floor as a service provider for the product to be built, intending to make the manufacturing process adaptable to changes. The model uses Reference nets as the modeling language, a high-level class of Petri nets, Java programming language as the annotation language, and free tool support. The model can be used to perform software-level simulations and can also be interconnected to existing physical devices using Internet of things technologies, enabling interactions between Cyber–Physical Systems (CPSs). It thus allows for the control of the shop floor and the reuse of the current machine park to make its adoption more sustainable. The model was used to generate several simulation results, which are presented and analyzed, thus demonstrating the model’s usefulness.

A Refined Siphon-Based Deadlock Prevention Policy for a Class of Petri Nets

Resource allocation systems (RASs) exist in various fields of modern society. The deadlock control problem is a crucial issue in control theory of RAS. This work is concentrated on a special class of shared resource and process-oriented Petri nets whose initial marking can have only a token in every resource place. Using mixed-integer programming (MIP) and iterative siphon control, we present a two-stage deadlock prevention policy. In particular, a modified MIP technique is developed for the first stage to compute a specific type of emptiable siphons and a siphon control method introducing monitors with related arcs whose weights all equal to one is established in the second stage. This policy leads to a maximally permissive liveness-enforcing supervisor and such an obtained controlled net is ordinary. Moreover, it avoids the exhaustive enumeration of siphons and the reachability analysis. Examples are provided to explain the policy.

Regular string token fuzzy Petri nets

Fuzzy Petri nets are a type of classical Petri nets designed to deal with imprecise and ambiguous data, that have been widely used to represent fuzzy production rules and fuzzy rule-based reasoning. In this paper, we introduce a new model called string token fuzzy Petri nets to generate fuzzy regular languages. Also, we study the equivalences of fuzzy regular grammar and regular string token fuzzy Petri net and establish some closure properties such as union, catenation, kleene closure, reversal, homomorphism and inverse homomorphism of the languages generated by the regular string token fuzzy Petri nets.