Verification of current-state opacity using Petri nets

Opacity is an important information-flow property, which is used to characterize whether or not the secrets of system have been leaked to the intruders. Over the past ten years, opacity of discrete event systems (DESs) modeled as automata and Petri nets have been well investigated under the assumption that the communication channels between systems and intruders are perfect. However, in a shared network, the communication delays and losses are inevitable usually. In this paper, we investigate the problem of opacity of networked discrete event systems (NDESs). We propose the notions of current-state opacity, initial-state opacity, initial-final-state opacity, and infinite-step opacity for NDESs. We also present the verification algorithms for these notions. Some examples are provided to illustrate the results obtained.

Verification of initial-state opacity in security applications of discrete event systems

Current-state opacity modelling and verification in partially observed Petri nets

State-Partition-Based Control of Discrete Event Systems for Enforcement of Regular Language Specifications

Opacity is important in investigating secrecy, privacy, and other properties in general systems that can be modeled as discrete event systems. To ensure opacity, a controller may be used to control information released to the public. For transparency and other reasons, it is often desired that the information released to the public be maximum, as long as opacity is not violated. In this paper, we investigate how to release the maximum information while ensuring opacity. We find a necessary and sufficient condition for an information release policy to ensure opacity. We also develop methods and algorithms to design a controller that releases maximum information. We consider both strong opacity and weak opacity. We apply the results to the dining cryptographers problem.

Individuals, populations and fluid approximations: A Petri net based perspective

Discrete event systems in applications, such as industry and supply chain, may show a very complex behavior. For this reason, their design and operation may be carried out by the application of optimization techniques for decision making in order to obtain their highest performance. In a general approach, it is possible to implement these optimization techniques by means of the simulation of a Petri net model, which may require an intensive use of computational resources. One key factor in the computational cost of simulation‐based optimization is the size of the model of the system; hence, it may be useful to apply techniques to reduce it. This paper analyzes the relationship between two Petri net formalisms, currently used in the design of discrete event systems, where it is usual to count on a set of alternative structural configurations. These formalisms are a particular type of parametric Petri nets, called compound Petri nets, and a set of alternative Petri nets. The development of equivalent models under these formalisms and the formal proof of this equivalence are the main topics of the paper. The basis for this formal approach is the graph of reachable markings, a powerful tool able to represent the behavior of a discrete event system and, hence, to show the equivalence between two different Petri net models. One immediate application of this equivalence is the substitution of a large model of a system by a more compact one, whose simulation may be less demanding in the use of computational resources.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

Security of distributed control systems is affected by the presence of information leaks, which permit to external intruders to infer the state of the system itself. Noninterference deals with the absence of such leak paths in a dynamic system modeled as discrete-event system. For a system that presents information leaks, a supervisory control strategy to enforce noninterference is proposed in this article. The approach is based on the solution of optimization problems on a Petri net model of the system under investigation. The effectiveness of the proposed enforcement strategy is shown by means of illustrative examples.

International audience

This paper presents an approach to perform Activity Based Costing (ABC) with Petri nets. ABC is a powerful methodology to calculate various of discrete event systems (e.g. production systems). Petri net models of discrete event systems are easy to create, comprehend, and to perform analysis, the mathematics behind Petri nets is also easy to grasp. This paper shows how ABC can be performed with Petri nets, so that various involved in a discrete event system can be easily measured with the help of the Petri net model. After a short introduction to ABC and Petri nets, this paper shows the approach which basically embeds various cost drivers as firing costs and firing times of transitions in a Petri net model. This work also presents a case study that is done with GPenSIM, a toolbox realized with this approach.

This paper is concerned with fault detection and location of discrete event systems (DES) modeled using interpreted Petri nets (IPN). The approach held deals with IPN models in which the marking is partially known. A diagnosis scheme that tracks the DES inputs and outputs is proposed; it allows detecting and locating an unexpected behavior within the DES. The diagnoser handles a monitoring model, expressed also as an IPN, which is computed from the DES model through an induced conservative marking law.

Many technological, industrial or economical systems are described by discrete event system (DES) models. The decision making processes that arise in the design and operation of this kind of systems can be afforded by means of algorithmic methodologies. A large range of approaches based on the simulation of the behavior of the system have been reported to answer this problem. Their main advantage consists of being applicable to most of the systems. An important drawback is the significant computational resources required to perform an exhaustive exploration of the state space due to the combinatorial explosion. A manual choice of a reduced set of configurations to be simulated can be improved by the use of parametric Petri nets and a metaheuristic search of the most promising ones. In this paper, a review of some definitions of parametric Petri net found in the literature is presented, as well as a definition for the general framework of stating optimization problems of both, the operation and the design of the model of the DES. Moreover, a methodology to obtain such a parametric Petri net, called compound Petri net, from an easier-to-obtain set of alternative Petri nets is proposed and an application example is given.

To observe occurrences of an event in a discrete event system, a sensor must be placed and activated. Both placement and activation incur costs. Assuming sensors have been placed, to minimize costs, one would like to minimize the activation of the sensors. In this paper, an online algorithm is developed to minimize sensor activation. The discrete event system under consideration is modeled by a finite automaton. The objective of observation is to distinguish certain pairs of states in the automaton, which are called a specification. This specification is extended to account for future evolution of the system under partial observation. Using the extended specification, the online algorithm presented needs only to look one step ahead and requires only to remember the current state estimate. The algorithm is of polynomial complexity at each step. The activation policy generated by the online algorithm is proved to be feasible, minimal, and to satisfy the specification. An example is presented to illustrate the results.

This paper presents the stabilization problem of discrete event systems modeled by Petri nets using the vector Lyapunov theory. After recalling some known stability information about discrete event systems modeled by Petri nets, the stabilization problem is addressed. A new promising methodology based on vector Lyapunov functions shows that it is possible to restrict the systems state space in such a way that boundedness is guaranteed. Moreover, the technique described can be used for regulation.