Petri net representation of multi-valued logical regulatory graphs

Relying on a convenient logical representation of regulatory networks, we propose a generic method to qualitatively model regulatory interactions in the standard elementary and coloured Petri net frameworks. Logical functions governing the behaviours of the components of logical regulatory graphs are efficiently represented by Multivalued Decision Diagrams, which are also at the basis of the translation of logical models in terms of Petri nets. We further delineate a simple strategy to sort trajectories through the introduction of priority classes (in the logical framework) or priority functions (in the Petri net framework). We also focus on qualitative behaviours such as multistationarity or sustained oscillations, identified as specific structures in state transition graphs (for logical models) or in marking graphs (in Petri nets). Regulatory circuits are known to be at the origin of such properties. In this respect, we present a method that allows to determine the functionality contexts of regulatory circuits, i.e. constraints on external regulator states enabling the corresponding dynamical properties. Finally, this approach is illustrated through an application to the modelling of a regulatory network controlling T lymphocyte activation and differentiation.     

Stochastic Petri net analysis of a replicated file system

The authors present a stochastic Petri net model of a replicated file system in a distributed environment where replicated files reside on different hosts and a voting algorithm is used to maintain consistency. Witnesses, which simply record the status of the file but contain no data, can be used in addition to or in place of files to reduce overhead. A model sufficiently detailed to include file status (current or out-of-date) as well as failure and repair of hosts where copies or witnesses reside, is presented. The number of copies and witnesses is not fixed, but is a parameter of the model. Two different majority protocols are examined     

A compact Petri net representation and its implications foranalysis

We explore a property-independent, coarsened, multilevel representation for supporting state reachability analysis for a number of different properties. This multilevel representation comprises a reachability graph derived from a highly optimized Petri net representation that is based on task interaction graphs and associated property-specific summary information. This highly optimized representation reduces the size of the reachability graph but may increase the cost of the analysis algorithm for some types of analyses. We explore this tradeoff. To this end, we have developed a framework for checking a variety of properties of concurrent programs using this optimized representation and present empirical results that compare the cost to an alternative Petri net representation. In addition, we present reduction techniques that can further improve the performance and yet still preserve analysis information. Although worst-case bounds for most concurrency analysis techniques are daunting, we demonstrate that the techniques that we propose significantly broaden the applicability of reachability analyses     

Real time identification of discrete event systems using Petri nets

The paper defines the identification problem for Discrete Event Systems (DES) as the problem of inferring a Petri Net () model using the observation of the events and the available output vectors, that correspond to the markings of the measurable places. Two cases are studied considering different levels of the system knowledge. In the first case the place and transition sets are assumed known. Hence, an integer linear programming problem is defined in order to determine a modelling the DES. In the second case the transition and place sets are assumed unknown and only an upper bound of the number of places is given. Hence, the identification problem is solved by an identification algorithm that observes in real time the occurred events and the corresponding output vectors. The integer linear programming problem is defined at each observation so that the can be recursively identified. Some results and examples characterize the identified systems and show the flexibility and simplicity of the proposed technique. Moreover, an application to the synthesis of supervisory control of systems via monitor places is proposed.     

Merged processes: a new condensed representation of Petri net behaviour

Model checking based on Petri net unfoldings is an approach widely applied to cope with the state space explosion problem. In this paper, we propose a new condensed representation of a Petri net’s behaviour called merged processes, which copes well not only with concurrency, but also with other sources of state space explosion, viz sequences of choices and non-safeness. Moreover, this representation is sufficiently similar to the traditional unfoldings, so that a large body of results developed for the latter can be re-used. Experimental results indicate that the proposed representation of a Petri net’s behaviour alleviates the state space explosion problem to a significant degree and is suitable for model checking.V. Khomenko is a Royal Academy of Engineering/Epsrc Research Fellow supported by the RAEng/Epsrc grant EP/C53400X/1 (Davac).M. Koutny is supported by the EC IST grant 511599 (Rodin).W. Vogler is supported by the DFG-project STG-Dekomposition VO 615/7-1     

A discrete Petri net model for cephalostatin-induced apoptosis in leukemic cells

Understanding the mechanisms involved in apoptosis has been an area of extensive study due to its critical role in the development and homeostasis of multi-cellular organisms. Our special interest lies in understanding the apoptosis of tumor cells which is mediated by novel potential drugs. Cephalostatin 1 is a marine compound that can induce apoptosis in leukemic cells in a dose- and time-dependent manner even at nano-molar concentrations using a recently discovered pathway that excludes the receptor-mediated pathway and which includes both the mitochondrial and endoplasmic reticulum pathways (Dirsch et al., Cancer Res 63:8869–8876, 2003; López-Antón et al., J Biol Chem 28:33078–33086, 2006). In this paper, the methods and tools of Petri net theory are used to construct, analyze, and validate a discrete Petri net model for cephalostatin 1-induced apoptosis. Based on experimental results and literature search, we constructed a discrete Petri net consisting of 43 places and 59 transitions. Standard Petri net analysis techniques such as structural and invariant analyses and a recently developed modularity analysis technique using maximal abstract dependent transition sets (ADT sets) were employed. Results of these analyses revealed model consistency with known biological behavior. The sub-modules represented by the ADT sets were compared with the functional modules of apoptosis identified by Alberghina and Colangelo (BMC Neurosci 7(Suppl 1):S2, 2006).     

Fault detection for discrete event systems using Petri nets with unobservable transitions

In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph.     

Modeling and formal verification of embedded systems based on a Petri net representation

In this paper we concentrate on aspects related to modeling and formal verification of embedded systems. First, we define a formal model of computation for embedded systems based on Petri nets that can capture important features of such systems and allows their representation at different levels of granularity. Our modeling formalism has a well-defined semantics so that it supports a precise representation of the system, the use of formal methods to verify its correctness, and the automation of different tasks along the design process. Second, we propose an approach to the problem of formal verification of embedded systems represented in our modeling formalism. We make use of model checking to prove whether certain properties, expressed as temporal logic formulas, hold with respect to the system model. We introduce a systematic procedure to translate our model into timed automata so that it is possible to use available model checking tools. We propose two strategies for improving the verification efficiency, the first by applying correctness-preserving transformations and the second by exploring the degree of parallelism characteristic to the system. Some examples, including a realistic industrial case, demonstrate the efficiency of our approach on practical applications.     

Implementation of real-time distributed control for discrete event robotic systems using Petri nets

This article presents a systematic method of modeling and implementing real-time control for discrete-event robotic systems using Petri nets. Because, in complex robotic systems such as flexible manufacturing systems, the controllers are distributed according to their physical structure, it is desirable to realize real-time distributed control. In this article, the task specification of robotic processes is represented as a system control-level net. Then, based on the hierarchical approach, it is transformed into detailed subnets, which are decomposed and distributed into the local machine controllers. The implementation of real-time distributed control through communication between the system controller and the machine controllers on a microcomputer network is described for a sample robotic system. The proposed implementation method is sufficiently general, and can be used as an effective prototyping tool for consistent modeling, simulation, and real-time control of large and complex robotic systems.     

Stochastic Petri net models of Ca2+ signaling complexes and their analysis

Mathematical models of Ca²⁺ release sites derived from Markov chain models of intracellular Ca²⁺ channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic Ca²⁺ excitability (i.e., puffs and sparks). Ca²⁺ release site models are composed of a number of individual channel models whose dynamic behavior depends on the local Ca²⁺ concentration which is influenced by the state of all channels. We consider this application area to illustrate how stochastic Petri nets and in particular stochastic activity networks can be used to model dynamical phenomena in cell biology. We highlight how state-sharing composition operations as supported by the M?bius framework can represent both mean-field and spatial coupling assumptions in a natural manner. We investigate how state-of-the-art techniques for the numerical and simulative analysis of Markov chains associated with stochastic Petri nets scale when modeling Ca²⁺ signaling complexes of physiological size and complexity.     

On fluidization of discrete event models: observation and control of continuous Petri nets

As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.     

On-line fault detection in discrete event systems by Petri nets and integer linear programming

The paper addresses the fault detection problem for discrete event systems in a Petri Net (PN) framework. Assuming that the structure of the PN model and the initial marking are known, faults are modelled by unobservable transitions. Moreover, we assume that there may be additional unobservable transitions associated with the system legal behaviour and that the marking reached after the firing of any transition is unknown. The proposed diagnoser works on-line: it waits for the firing of an observable transition and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behaviour is normal or exhibits some possible faults. The results characterize the properties that the PN modelling the system fault behaviour has to fulfill in order to reduce the on-line computational effort.     

Stochastic colored Petri net models of flexible manufacturing systems: Material handling systems and machining

This paper presents an overview of SCPN theory, a set of three generic SCPN submodels, a behavior-preserving methodology for combining those submodels into a larger model, and a combined model. The three submodels include a machine with failures, repairs, and limited I/O buffers, and two types of conveyor submodels—a simple conveyor segment and a conveyor segment at a machine.     

A Petri net representation of Bayesian message flows: importance of Bayesian networks for biological applications

This article combines Bayes’ theorem with flows of probabilities, flows of evidences (likelihoods), and fundamental concepts for learning Bayesian networks as biological models from data. There is a huge amount of biological applications of Bayesian networks. For example in the fields of protein modeling, pathway modeling, gene expression analysis, DNA sequence analysis, protein–protein interaction, or protein–DNA interaction. Usually, the Bayesian networks have to be learned (statistically constructed) from array data. Then they are considered as an executable and analyzable model of the data source. To improve that, this work introduces a Petri net representation for the propagation of probabilities and likelihoods in Bayesian networks. The reason for doing so is to exploit the structural and dynamic properties of Petri nets for increasing the transparency of propagation processes. Consequently the novel Petri nets are called “probability propagation nets”. By means of examples it is shown that the understanding of the Bayesian propagation algorithm is improved. This is of particular importance for an exact visualization of biological systems by Bayesian networks.     

借助Petri网进行流程审计

信息的使用者往往关注保存在介质上的信息而忽视处理信息的程序。由于保存在介质上的信息有多个操作入口,即使处理信息的程序真实地反映了组织的业务流程,也难保证信息使用者所获得的信息是正确的,也就是说对于访问数据的程序,存在外部干扰。引入数据库中的审计表功能,协助信息系统审计人员识别信息系统中数据的形成是否遵循了既定的业务流程。由于Petri网是描述流程的有力工具,对于复杂的业务流程,引入Petri网对流程进行审计是必要的。     

Canonical prefixes of Petri net unfoldings

In this paper, we develop a general technique for truncating Petri net unfoldings, parameterized according to the level of information about the original unfolding one wants to preserve. Moreover, we propose a new notion of completeness of a truncated unfolding. A key aspect of our approach is an algorithm-independent notion of cut-off events, used to truncate a Petri net unfolding. Such a notion is based on a cutting context and results in the unique canonical prefix of the unfolding. Canonical prefixes are complete in the new, stronger sense, and we provide necessary and sufficient conditions for its finiteness, as well as upper bounds on its size in certain cases. A surprising result is that after suitable generalization, the standard unfolding algorithm presented in [8], and the parallel unfolding algorithm proposed in [12], despite being non-deterministic, generate the canonical prefix. This gives an alternative correctness proof for the former algorithm, and a new (much simpler) proof for the latter one.Received: 29 April 2003, Published online: 2 September 2003     

Discrete Time Stochastic Petri Nets

Basic graph models of processes, such as Petri nets, have usually omitted the concept of time as a parameter. Time has been added to the Petri net model in two ways. The timed Petri net (TPN) uses a fixed number of discrete time intervals. The stochastic Petri net (SPN) uses an exponentially distributed random variable. In this paper, a discrete time stochastic Petri model is described. These discrete time SPN's fill the gap between TPN and normal SPN. However, the use of discrete time complicates the SPN model in that more than one transition may fire at a time step. Finally, an example of a live and bounded Petri net which has nonempty, disjoint, recurrent subsets of markings is given.