Petri Net Structure Research Articles

Exploiting the structure of biochemical pathways to investigate dynamical properties with neural networks for graphs.

Dynamical properties of biochemical pathways (BPs) help in understanding the functioning of living cells. Their in silico assessment requires simulating a dynamical system with a large number of parameters such as kinetic constants and species concentrations. Such simulations are based on numerical methods that can be time-expensive for large BPs. Moreover, parameters are often unknown and need to be estimated. We developed a framework for the prediction of dynamical properties of BPs directly from the structure of their graph representation. We represent BPs as Petri nets, which can be automatically generated, for instance, from standard SBML representations. The core of the framework is a neural network for graphs that extracts relevant information directly from the Petri net structure and exploits them to learn the association with the desired dynamical property. We show experimentally that the proposed approach reliably predicts a range of diverse dynamical properties (robustness, monotonicity, and sensitivity) while being faster than numerical methods at prediction time. In synergy with the neural network models, we propose a methodology based on Petri nets arc knock-out that allows the role of each molecule in the occurrence of a certain dynamical property to be better elucidated. The methodology also provides insights useful for interpreting the predictions made by the model. The results support the conjecture often considered in the context of systems biology that the BP structure plays a primary role in the assessment of its dynamical properties. https://github.com/marcopodda/petri-bio (code), https://zenodo.org/record/7610382 (data).

Performance analysis of Petri net based on moment generating function

The Petri net structure of workflow is used to model, and the moment generating function is used to analyze the time performance of workflow, and the complexity of analysis is given. It provides basic theory and basis for analysis and verification. The calculation of time complexity is given for sequence, concurrency, cycle, conflict (selection) and mutual exclusion. The performance analysis method based on moment generating function can be used to analyze the performance of arbitrarily distributed bounded or unbounded random Petri nets. Establish a broad-random Petri net model that conforms to the concept of workflow. Then, based on statistical analysis and experience estimation of relevant data in the actual system, analyze the time nature of the on-demand service based on the analysis method based on behavioral expression, and obtain some valuable performance and index information. A necessary and sufficient condition for maintaining reliability of a workflow network model is given; A polynomial decomposition algorithm for P-invariants is proposed; Combining the moment function, a performance analysis method for workflow systems is established. An example is given to verify the effectiveness of the algorithm.

Public bicycle sharing systems control and performance evaluation: A Petri net-based approach

Public bicycle sharing systems (PBSS) allow citizens to move between two points within a region using bicycles, being composed of stations where users can either pick up or return bicycles after using them. Depending on the demand for bicycles, stations may either become empty or full of bicycles. This problem is usually solved by means of a vehicle that exchanges bicycles among the stations following some balancing strategy. In this paper, we propose a model for PBSSs using generalized stochastic Petri nets with external control, a Petri net with an external agent that decides how to execute the balancing strategy. The main advantage of our model is that it allows different balancing strategies to be implemented without changing the Petri net structure. In addition, since the model is a Petri net, we can easily implement it by making a Petri net simulator built with the incidence matrix associated with the Petri net model. We also propose two balancing strategies and validate both the simulation algorithm and the balancing strategies by applying them to the performance evaluations of the model of a real system, named Integra UFRJ PBSS. The performance evaluation of the system under the balacing strategies have shown that both strategies considerably reduce the times, in average, that stations remain full or empty throughout the system operation, solving problems related to stations being empty of full; in particular, the first strategy reduced those times in such a way that no more than five percent of the users of each station had trouble returning their bicycles due to stations being full, whereas the second strategy reduced the percentage of lost users due to stations being empty to no more than five percent for each station.

Concurrency and Petri Net Models

Concurrency is a fundamental problem and a solution applicable to different areas of computing. Given the complexities and distribution of computer systems and services, concurrency is a modern area requiring proper attention. Petri nets are formalisms based on process representation both from a mathematical view and from a graphical or drawing like view. Petri nets are used to model concurrent processes. This work deals with understanding and representing low level concurrency in Petri nets, when this is not always visible and properly noted from the graphical structure. In this study an algebraic notation has been devised and is used to represent the Petri net structures. This algebraic notation is used as an alternative and simplified way of representation. The notation is explained and several simple examples are given. The notation presented can be used in conjunction with other Petri net analysis and verification methods. Some results and findings are discussed.

Modeling Analysis of SM2 Construction Attacks in the Open Secure Sockets Layer Based on Petri Net.

The detection and defense of malicious attacks are critical to the proper functioning of network security. Due to the diversity and rapid updates of the attack methods used by attackers, traditional defense mechanisms have been challenged. In this context, a more effective method to predict vulnerabilities in network systems is considered an urgent need to protect network security. In this paper, we propose a formal modeling and analysis approach based on Petri net vulnerability exploitation. We used the Common Vulnerabilities and Exposures (CVE)-2021-3711 vulnerability source code to build a model. A patch model was built to address the problems of this model. Finally, the time injected by the actual attacker and the time simulated by the software were calculated separately. The results showed that the simulation time was shorter than the actual attack time, and ultra-real-time simulation could be achieved. By modeling the network system with this method, the model can be found to arrive at an illegitimate state according to the structure of Petri nets themselves and thus discover unknown vulnerabilities. This method provides a reference method for exploring unknown vulnerabilities.

Quotient Petri nets*

This work introduces the concepts of quotient Petri net (QPN) and dual quotient Petri net (DQPN) as tools to build abstractions of Petri net (PN) structures with three different purposes: a) to have an abstraction (dynamic congruence) of a PN, b) to obtain distributed representations of systems; c) to remove undesired system dynamics. The main advantages are: a) QPN and DQPN preserve sufficient information of the original PN enabling engineers to implement hierarchical or distributed controllers, observers, diagnosers, etc. schemes avoiding/reducing centralized coordinators, b) QPN and DQPN can be efficiently computed by using linear transformations. In fact, a method for computing QPNs and DQPNs is introduced. This work introduces a methodology to compute QPNs and DQPNs that preserve the consistent and conservative from the original PNs.

Exploiting symmetries of high-level Petri games in distributed synthesis

Abstract Distributed Synthesis is the problem of automatically generating correct controllers for individual agents in a distributed system. Petri games model this problem by a game between two teams of players on a Petri net structure. Under some restrictions, Petri games can be solved by a reduction to a two player game. The concept of symmetries in Petri nets is closely related to high-level representations of Petri games. Applying symmetries to the states in the two-player game results in a significant state space reduction. We give an overview about (high-level) Petri games and the application of symmetries in this setting. We present ongoing work aiming to concisely describe solutions of Petri games by a high-level representation.

Graph Drawing Approaches for Petri Net Visualisation and Representation

Petri net structures can benefit from being modelled using graph drawing approaches. This work presents some advanced graph drawing approaches that can be used for visualising Petri net models. These are i) topological shape metrics, ii) visibility drawing, iii) orthogonalization, iv) hierarchical and v) bi-graph partitioning. The models show that this can be successfully done and the Petri nets that are generated in this work are suitable for visualisation. Graph visualisation is an important topic and the results show that there is a large potential to apply this approach to drawing Petri Nets in novel ways.

On computing the supremal right-closed control invariant subset of a right-closed set of markings for an arbitrary petri net

A set of non-negative integral vectors is said to be right-closed if the presence of a vector in the set implies all term-wise larger vectors also belong to the set. A set of markings is control invariant with respect to a Petri Net (PN) structure if the firing of any uncontrollable transition at any marking in this set results in a new marking that is also in the set. Every right-closed set of markings has a unique supremal control invariant subset, which is the largest subset that is control invariant with respect to the PN structure. This subset is not necessarily right-closed. In this paper, we present an algorithm that computes the supremal right-closed control invariant subset of a right-closed of markings with respect to an arbitrary PN structure. This set plays a critical role in the synthesis of Liveness Enforcing Supervisory Policies (LESPs) for a class of PN structures, and consequently, the proposed algorithm plays a key role in the synthesis of LESPs for this class of PN structures.

On Hierarchical Construction of the State Space of an Automated Manufacturing System Modeled With Petri Nets

State space techniques are one of the main approaches deployed for the analysis of concurrent systems. However, state space construction is stalled by a common phenomenon called the state explosion problem which makes it a tough task or even impossible when the state space computation demands prohibitive cost (time and memory). We limit general resource allocation systems (RASs) to a certain class whose state space can be hierarchically constructed, yet it comprises various enough types of real-world discrete event systems, such as automated manufacturing systems. This paper focuses on a class of RASs modeled with Petri nets (PNs), where, through pure algebraic operations, a novel method to compute the state spaces is proposed, which is motivated by the superposition property. Given a PN model of a system and a target resource configuration, we first propose a special initial marking called the initial basis marking and compute the corresponding reachability graph. Then, we increase the capacity of the resource places in an incremental way and generate the reachability graphs by taking advantage of the PN structure and the previously computed reachability graph until the capacity function of resources reaches the target resource configuration. A complete enumeration of reachable states can be obtained by a recursive scheme. Experimental studies also demonstrate the efficiency of the proposed approach in terms of computational cost and its high-potential to cope with the state-explosion problem.

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.

On Liveness Enforcing Supervisory Policies for Arbitrary Petri Nets

Neither the existence nor the nonexistence of a liveness enforcing supervisory policy (LESP) for an arbitrary Petri net (PN) is semidecidable. In an attempt to identify decidable instances, we explore the decidability of certain properties of the set of initial markings for which an LESP exists, and the decidability of the existence of a specific class of LESPs. We first prove that for an arbitrary PN structure, determining if there is an initial marking, or there are no initial markings, for which there is an LESP, is not semidecidable. Then, we characterize the class of PN structures for which the set of all initial markings for which an LESP exists is right-closed . We show that testing membership, or nonmembership, of an arbitrary PN in this class of PNs is not semidecidable. We then consider a restricted class of LESPs, called marking monotone LESPs (MM-LESPs). We show that the existence of an MM-LESP for an arbitrary PN is decidable.

A Petri Net Neural Network Robust Control for New Paste Backfill Process Model

In mining industries, the backfill becomes more and more important due to the environment protection concern. But most backfill investigations focus on the underground model and backfill materials. In this research, the paste backfill process based on the process control is investigated and a new paste backfill process model is proposed according to the Torricelli's law and Bernoulli principle. In order to deal with the unknown nonlinear function of the proposed backfill model, a Petri net(PN) structure is presented and a new Petri net neural network(PNNN) is introduced to approximate the unknown nonlinear function. Then, a robust controller is designed for the backfill process with PNNN and the closed loop stability is guaranteed by Lyapunov function candidate. The effectiveness of the proposed model with new PNNN and the robust controller are verified by simulation results.

Adjunct Octagonal Array Token Petri Nets

Adjunct Octagonal Array Token Petri Net Structures (AOATPN) are recently started out octagonal photograph delivering structures which out prolonged the Octagonal Array Token Petri internet systems. on this paper we view as AOATPN format over a control feature named inhibitor curves and separate it amongst a few critical octagonal photograph making and perceiving designs regarding the making energy.

Hybrid approach for detection of malicious profiles in twitter

Emergence of social media invokes social actors to share their information digitally. Moreover, it enables them to maintain their links with other people worldwide. Due to its massive popularity, it has become a fascinating test bed to initiate various attacks. Attackers form Sybil nodes to disseminate malicious content in order to infect legitimate users aiming to steal sensitive information, such as user's credentials. Therefore, the focus of this paper is to detect malicious profiles, specifically on the Twitter microblogging platform. We propose a hybrid approach which leverages the capabilities of machine learning techniques to identify malicious profiles. Initially, Petri net structure analyzes the user's profile and various features, and these features are then used to train classifier. This is achieved to identify malicious profiles from legitimate users. Finally, to prove the efficiency, a comparative analysis of our approach is conducted with existing state-of-the-art techniques. The experimental results reveal that our approach achieves a high detection rate of 99.16% which is better than other techniques.

Modules of Petri nets and new Petri net structure: Arcs with a weighted function set

This article addresses expressiveness problems for Petri nets and their useful extension for modeling and control of a system that can be modeled with Petri nets. We construct some Petri net modules, namely, an enabling module, an inhibitor module and a Modulo-N counter, which are useful for system operations. We also present the simplifications for the enabling and inhibitor modules. Then, we propose two new types of arcs, namely, enabling and inhibitor arcs, with a weighted function set. The arcs with the weighted function set from places to transitions are the marked arcs. A function set is employed to denote the weight of an arc according to the system requirements. They are very useful to solve the resource reallocation problem in a resource allocation system, where resource sharing contributes to the occurrences of deadlocks. Finally, two examples are used to show the advantages of the presented new types of arcs.

Modeling of Real-time Process Control

This paper discusses the successive steps used for modeling a real-time system. The term control means the of a by a -computer-. The real time process is distinguished from other types of processes by two basic features the fast response to sudden external events is an essential criterion, and - the order in which the external events are occurir,g is the main critical factor [3] These two private characteristics impose a set of conditions on the system response. The simultaneous occurence of events, must not result a random response. A predetermined action is necessarily decided. Evidently, a successful system design starts by depicting the functional specifications into a suitable functional model. It is'nt enough to have a clear model, but it must be also free of problems. The possible problems can be detected and avoided by analysing the resulting model. The modeling tool which has a set of powerful analysis rules, is the Petri net. The Petri net structure proved effecient use in system modeling. The chosen application,on the modeling procedure presented in the paper, is a double runway system. A hierarchical construction of the model is illustrated with detailed explain-ation. This modeling procedure can be similarly applied to any other system.

Minimum Initial Marking Estimation in Labeled Petri Nets With Unobservable Transitions

In the literature, researchers have been studying the minimum initial marking (MIM) estimation problem in the labeled Petri nets with observable transitions. This paper extends the results to labeled Petri nets with unobservable transitions (with certain special structure) and proposes algorithms for the MIM estimation (MIM-UT). In particular, we assume that the Petri net structure is given and the unobservable transitions in the net are contact-free. Based on the observation of a sequence of labels, our objective is to find the set of MIM(s) that is(are) able to produce this sequence and has(have) the smallest total number of tokens. An algorithm is developed to find the set of MIM(s) with polynomial complexity in the length of the observed label sequence. Two heuristic algorithms are also proposed to reduce the computational complexity. An illustrative example is also provided to demonstrate the proposed algorithms and compare their performance.

Stability Analysis of Discrete Event Systems Modeled by Petri Nets Using Unfoldings

The stability of discrete event systems (DESs) is a property related to its robustness; a stable DES is guaranteed to reach a set of desired states in a finite number of steps. Algorithms proposed in the literature are useful for analyzing the stability of DES modeled either by finite automata or a constrained subclass of Petri nets (PNs). In this paper, a novel method to decide the stability of safe PNs is presented. It is based on the analysis of the finite complete prefix of the net unfolding rather than the reachability graph. For concurrent systems, the prefix is usually smaller than the reachability graph and then the analysis using the proposed algorithm is more efficient than analyzing the reachability set of the PN. Note to Practitioners —The stability of a discrete event system (DES) is a property that guarantees that the DES will return to the normal operation behavior after a disturbance deviates the system from such a behavior. This is a key property that a controlled DES must fulfill. The algorithms proposed in this paper allow determining efficiently the stability of concurrent DES by analyzing the Petri net structure.

Structural Decomposition and Decentralized Control of Petri Nets

Control of a large-scale automated manufacturing system is an important and challenging issue. Its discrete event system model represented by Petri nets tends to become highly complicated in structure, especially when there exist uncontrollable or unobservable events. The existing approaches are nontrivial to design both efficient and maximally permissive supervisors to impose constraints on an overall system. In this paper, instead of considering the control problem from an overall system perspective, we intend to transform an overall control problem into the one designing multiple controllers in parallel, each of which is much simpler in structure. A Petri net structure is decomposed via integer linear programming or a polynomial decomposition method to obtain multiple state-machine subnets that constitute a decentralized system. A necessary and sufficient condition for preserving the equivalence in terms of states and behaviors between the overall system and its decentralized version is reported. Constraints representing control requirements are further converted and enforced in the respective subnets. Then, supervisors are generated via a generalized mutual exclusion constraint method. By considering the deviations between the subnet control and overall control, this paper formulates a communication mechanism to guarantee that the decentralized system runs in an appropriate manner. Finally, two examples are presented to demonstrate the proposed approach.