Verifying system security using Petri Nets

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.

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.

Modeling computer software, hardware, and other systems using Petri nets is discussed. The various analysis techniques and extension of Petri nets are considered. Problems in Petri net analysis techniques are examined, and analysis techniques that solve them are given.

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.

With the aim of solving the problems of the Petri nets to the place/transition nets automatic conversion and realization of Petri nets parallel control and running, the algorithm is proposed to transform Color Petri net systems transform into P/T nets. The algebraic model of colored Petri nets and P/T nets, and its intrinsic mechanism is analyzed, the process and theory verification of the colored Petri nets into P/T nets are given. The colored Petri nets into P/T network algorithm is proposed, through the network model of formal, colored Petri nets correlation matrix pretreatment. Experimental results show that it is an effective method to solve Color Petri Net systems transform into P/T nets, lay the foundation for various senior Petri nets system transformation into P/T nets and achieve the parallelism and simulation of running.

The context of our work is the complex systems simulation. Complex systems modelling and simulation require to take into account the interactions between the different components. For instance, an airport ground traffic simulation requires to model the planes with the pilots, the control tower, the

Petri Nets provide a graphical notation for modeling systems and performing analysis. Colored Petri Nets (CPNs) combine the strengths of ordinary Petri Nets with a high level programming language, making them more suitable for modeling large systems. A CPN model is an executable representation of a system that can be analyzed through simulation. CPN models are built using CPN Tools, a graphical software tool and interface used to create, edit, simulate, and analyze models. This tutorial is meant to introduce the reader to the vocabulary and constructs of CPNs and illustrate the use of CPN Tools in creating and simulating models by means of a familiar, simple example. In particular, we show how to create a CPN model of the call center example presented by White and Ingalls in their tutorial Introduction to Simulation.

The travelling salesman problem, which can be solved with various methods, is a traditional and typical problem in artificial intelligence (AI). As an evolution of Petri nets, colored Petri nets (CPN) can be dedicated to modeling and analysis of different systems as a new attempt. The paper shows the brief description of the given problem and CPN, we detail the implementation of the CPN model of the problem and analyze the simulation result. This CPN example shows the potentiality of CPN application in AI.

The authors propose a safety analysis method using coloured Petri nets (CPN). Their method employs a backward approach where a hazard is assumed to have occurred and backward simulation from the hazard is performed in order to determine if and how the hazard might occur. Using CPN, they define a hazard as a set of markings and perform backward simulation by generating a reachability graph backwards from the hazard. To facilitate the safety analysis, they extend the semantics of CPN and define backward reachability graphs of CPN. To demonstrate their method, a shutdown system for a Korean nuclear power plant is used as an example.

Specification and properties of a cache coherence protocol model.- GAMERU: A language for the analysis and design of human communication pragmatics within organizational systems.- Recent results on the complexity of problems related to Petri nets.- Algebraic structure of flows of a regular coloured net.- On equivalent execution semantics of concurrent systems.- Mathematical methods for calculating invariants in Petri nets.- On Petri nets with deterministic and exponentially distributed firing times.- An accurate performance model of CSMA/CD bus LAN.- Petri net models for the ?-calculus.- Fair processes.- Operational Petri net semantics for CCSP.- Infinitary languages of Petri nets and logical sentences.- A strong part of concurrency.- Concurrency and continuity.- Parallel systems specifications with coloured Petri nets and algebraic specifications.- Bibliography of Petri nets.

Petri net (PN) is a classical tool for modeling, simulation, and analysis. With the emergence of distributed manufacturing system (DMS), PN has been evolved into different forms such as colored PN (CPN) and timed PN (TPN). To fulfill the practical requirements, CPN has been extended to a larger and more complex model. Meanwhile, DMS becomes an important issue for industry, and how to model a complex manufacturing network for better throughput needs further investigation. A simple single type of PN only cannot fulfill all contemporary requirements at the same time. This paper proposes a new concept for a new PN-hierarchical timed CPN (HTCPN), which can be a powerful tool for modeling, simulation, and analysis for current large complex distributed manufacturing system. This paper presents a general structure of DMS and uses HTCPN to model the manufacturing system as discrete event with dynamic behavior. The proposed approach shows superiority on modeling large complex manufacturing system as it represents the material flow and transitions clearly and provides overview and detailed description for DMS.

In this work, the analysis of behavioural and structural features of automated systems has been investigated by using coloured Petri Nets (CPNs). CPN is one of the best modelling methods of the automated system. Many features of Petri Nets can be searched by reachability tree and invariants. They also show the features of CPN. Reachability tree shows the markings which can be reached by the net. With P invariants we can determine the correctness of the net. In this work, an algorithm to calculate reachability tree of automated systems is developed. P invariants of CPN is analysed and Martinez-Silva algorithm is applied to CPNs. Time performances of these methods are also determined.

The paper is a partial synthesis of the work that a team within the Faculty of Managerial and Technological Engineering has in the field of modeling and simulation of systems with Petri nets. The paper deals with three issues. The first part is Modeling and simulation of manufacturing systems with timed Petri nets. The first part presents the way in which the performances of some manufacturing systems are evaluated using timed Petri nets. The first example is a manufacturing system specific to the textile industry. The system has three production lines. In this case, the modeling with timed Petri nets allows the analysis of the operation of the flow lines and highlights the bottleneck. Another modeled manufacturing system is specific to a series production, more precisely it refers to the manufacture of gas cookers within a company from Oradea. The model with Petri nets also describes the supply sequences of the stocks of parts and subassemblies. The next modeled system is an automated manufacturing system for the packaging of detergents. The complexity of the Detergent Packing System and the high level of automation, require the use of efficient modeling and simulation methods to verify the validity of the solutions adopted. In this chapter is present the model of a robotic welding cell. The second part of the paper, the transition from timed Petri nets to hierarchical colored Petri nets, shows how Petri nets were developed for a robotic cell for metallographic analysis. The third part is dedicated to modeling with colored Petri nets timed with complex colors of the flexible manufacturing cell A007 within the Department of Industrial Engineering.

Behaviour Equivalent Max-Plus Automata for a Class of Timed Petri Nets

Discrete event systems are modeled compactly by using Petri nets (T. Murata, 1989). Although Petri nets have powerful mathematical verification ability, in many cases, we have to construct the whole state space for verification. A reachability graph is one of the representations of the state space. Petri nets can describe huge systems compactly, but sometimes it is impossible to generate the reachability graph because of an explosion in required computational time and space. A Petri net is called a reversible net, when it can come back to the initial marking from any reachable marking. The paper considers a verification method for reversibility. An unfolding is obtained by unfolding a Petri net, and it preserves reachability information of an original net and structural analysis on it is much easier than on the original net. The article clarifies relations between unfoldings and reversibility, and provides a verification method for reversibility by using unfoldings.