Knowledge-based approach to Petri nets analysis

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.

Petri nets are a well established mod- elling technique for analyzing parallel systems. When coupled with an event-driven operatine system, Petri nets can provide an effective means for integrating and controlling the functions of distributed robotic appli- cations. Recent work has shown that Petri net graphs can also serve as remarkably intuitive operator inter- faces. In this paper the advantages for using Petri net as high-level controllers to coordinate robotic functions will be outlined; the considerations for designing Petri net controllers will be discussed; and simple Petri net structures for implementing an interface for operator supervision will be presented. I. INTRODUCTION The Theory of Intelligent Machines, as proposed in (8), describes a hierarchical organization of the functions of an autonomous robot into three levels: an Execution Level containing the hardware and basic control functions, a Coordination Level integrating the capabilities of the in- telligent machine (IM) across hardware systems, and an Organization Level providing higher-level planning and reasoning capabilities. Figure 1 illustrates this hierarchi- cal organization. An analytic formulation of the theory using information-theoretic measures of uncertainty for each level of the intelligent machine has been developed in recent years 9)(10). A long-term research goal of the ration (CIRSSE) is to attempt, guided by these theories, implementations of autonomous robots. In the past year at CIRSSE a computer architecture was developed that implements the lower two levels of the in- telligent machine (4). The architecture supports an event- Center for Intel I igent Robotic Systems for Space Explc-

Given an initial marking and final marking for a Petri net model, an optimal firing sequence problem is defined as the problem to find an optimal transition firing sequence to minimize the objective function. For the purpose of analysis of general integer programming problems, we propose a Petri net representation and reachability analysis of integer programming problems. In the proposed method, an integer programming problem is converted into the optimal firing sequence problem of Petri nets. By utilizing the proposed algorithm, integer programming problems can be visualized and analyzed by the Petri net theory. We apply the proposed methodology to the scheduling problems of dual armed cluster tools. The valid inequalities are derived from the reachability analysis. Numerical results show that those valid inequalities can significantly reduce the computational time of the original integer programming problem.

Analysis approaches of reachability decision is fundamental to Petri nets theory; however, the relevant research work in the past cannot always guarantee the correctness of analysis conclusions. This paper firstly reveals the root cause of wrong conclusions, which are drawn in analysis for deadlock of Petri nets based on modified reachability trees (MRT), and then proposes the rectified calculation of the next-state function and some corresponding definitions, which guarantee MRT's usefulness and correctness in analyzing reachability and deadlock of one-place unbounded Petri nets. Finally, a necessary and sufficient condition of MRT's reachability and the theoretical proof are presented. Examples are given to illustrate the method.

The resource scheduling problem becomes complex, as resources are distributed, heterogeneous, dynamic and autonomous. A resource scheduling scheme with three-level for grid computing is proposed in this paper by analyzing present resource scheduling scheme. Petri net is a powerful graphical and mathematics tool for describing the concurrent, asynchronous and dynamic events. This paper models and analyzes the resource scheduling scheme of grid computing using hierarchical Petri net. Different Petri net models for resource scheduling of different layers are given in this paper. Petri model for different layer has different behavior, which represents heterogeneous and autonomous features of grid computing resources. Finally, we get some important results such as throughput, load balance and makespan on resource scheduling by analyzing reachability of Petri nets.

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.

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

Based on the workflow management coalition (WFMC) standard and component software technologies, this paper addresses our Petri-nets-based approach for workflow and process automation. Petri nets provide graphical and mathematical formalisms for work-flow process definition and analysis. In this paper, we will present how to use Petri nets and a toolkit NCUPN (National Central University Petri Nets toolkit) for process definition and analysis. NCUPN is a Petri nets modeling and analysis toolkit developed to help software engineers in drawing and doing analysis. Once a workflow process is drawn using NCUPN, analysis can be done automatically. In this paper, we will demonstrate how to use NCUPN to analyze behavioral properties of workflow process, such as deadlock, liveness, safety, and starvation.

This article provides a computational framework to model self‐adaptive expert systems using the Petri net (PN) formalism. Self‐adaptive expert systems are understood here as expert systems with the ability to autonomously learn from external inputs, like monitoring data. To this end, the Bayesian learning principles are investigated and also combined with the Plausible PNs (PPNs) methodology. PPNs are a variant within the PN paradigm, which are efficient to jointly consider the dynamics of discrete events, like maintenance actions, together with multiple sources of uncertain information about a state variable. The manuscript shows the mathematical conditions and computational procedure where the Bayesian updating becomes a particular case of a more general basic operation within the PPN execution semantics, which enables the uncertain knowledge being updated from monitoring data. The approach is general, but here it is demonstrated in a novel computational model acting as expert system for railway track inspection management taken as a case study using published data from a laboratory simulation of train loading on ballast. The results reveal self‐adaptability and uncertainty management as key enabling aspects to optimize inspection actions in railway track, only being adaptively and autonomously triggered based on the actual learnt state of track and other contextual issues, like resource availability, as opposed to scheduled periodic maintenance activities.

Problems such as low transport efficiency, low safety factor, and difficulty in the dispatching of hybrid locomotives, which are not optimal in the automated transport of coal mines, are always difficult to study. These serious situations are studied and avoided through petri net (PN) analysis techniques in this paper. Firstly, by analyzing the relationship between locomotives, road sections and elements of petri net, petri net scheduling mode is built for locomotives with three different routes according to three different mine locomotive scheduling methods. Then, based on a certain set of resources in PN, the concepts of a deadlock state equation and a potential deadlock state equation are introduced. The deadlock state equation describes the intrinsic relationship between resources assignation and a deadlock state in PN. This equation is a necessary and sufficient condition for the occurrence of a deadlock situation. In the following part, the deadlock equations of several network models are solved, and the deadlock verification is carried out using the software PIPE, which proves the validity of the equations. The results show that the solution of the deadlock equation and the potential deadlock equation can effectively avoid the deadlock of petri net model, so as to prevent the blocking and collision of locomotives. At the same time, the whole modeling process also verifies the effectiveness of petri net for mining bottom locomotive modeling.

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent, dedicated algorithms which have been designed to operate modularly, portably, extensibly, and efficiently.

Timed Petri nets can be used to model and analyse scheduling problems. To support the modelling of scheduling problems, we provide a method to map tasks, resources and constraints onto a timed Petri net. By mapping scheduling problems onto Petri nets, we are able to use standard Petri net theory. In this paper we will show that we can use Petri net based tools and techniques to find conflicting and redundant precedences, upper- and lower-bounds for the makespan, etc. This is illustrated by a Petri net based analysis of the notorious 10×10 problem due to Fisher & Thompson (1963)

The article describes a part of our research in the area of (business) process modeling, analysis and execution. It describes the current state of process languages and standards. It concentrates on the process model interoperability and portability problems, caused because of huge number of process modeling standards, which often do not even target the same conceptual level of process modeling. It provides an idea how to bring together those standards, using process concepts mapping into Petri nets and incorporating the usage of process patterns. Transformation to strictly formal process languages has a potential to prove itself as a fair solution with the following advantages: the number of mappings among different process languages is reduced and the process model can be analyzed using proven Petri Net or general graph algorithms. Development of the approach is still in its early phase. Mapping rules to/from process patterns are neither strictly defined nor trivial, therefore, they will be the main focus of our future research.

CORBA is a standard proposed by the Object Management Group (OMG) that promotes interoperability between distributed object systems. Following the standardization of this object-oriented middleware, the OMG has specified a set of Common Object Services (COS) that are meant to serve as the building blocks of distributed CORBA applications. The COSes are specified using CORBA Interface Definition Language (IDL), that describes the syntactic aspects of services supported by remote objects. However, CORBA-IDL does not support specification of the behaviour of objects in an abstract and formal way, and behavioural specification is mostly provided in plain English. To overcome this problem, we have proposed a formal description technique (Cooperative Objects) based on high-level Petri nets, and developed a software support environment. The goal of this paper is to demonstrate that our approach is suited to the formal specification of typical CORBA COS, and presents a Cooperative Object model of the CORBA event service, a COS that provides asynchronous, one-to-many communication between objects. The advantages of dealing with a tool-supported, executable formal notation are detailed, as well as the results that can be obtained through Petri net analysis techniques.Key wordsDistributed systemsbehavioural specificationCORBAhigh-level Petri nets

This paper proposes a fully expanded tree (FET) approach for one-place-unbounded Petri nets. The FET of a one-place-unbounded Petri net consists of all and only reachable markings from its initial marking. Its applications to liveness and deadlock analysis for such Petri nets are developed. The proposed method has a larger application scope than all the existing methods for them. Several examples are provided to show its superiority over the state-of-the-art methods.