Dynamically consistent reduction of logical regulatory graphs

To cope with the increasing complexity of regulatory networks, we define a reduction method for multi-valued logical models.Starting with a detailed model, we use decision diagrams to compute reduced models by iteratively “removing” regulatory components. To keep a consistent dynamical behaviour, the logical rules associated with the targets of each removed node are actualised to account for the (indirect) effects of its regulators.This construction of reduced models preserves crucial dynamical properties of the original model, including stable states and more complex attractors. In this respect, the relationship between the attractor configuration of the original model and those of reduced models is formally established. We further analyse the issue of attractor reachability.Finally, we illustrate the flexibility and efficiency of the proposed reduction method by its application to a multi-valued model of the fly segment polarity network, which is involved in the control of segmentation during early embryogenesis.     

Using Petri net graphs express boolean functions

Both the combination and sequential switching function, also called switching circuits, can be represented by the binary code with Boolean algebra and Finite State Machine （FSM）. The basic elements of Petri net graph, such as place nodes, transition nodes, arcs, and tokens are used to frame the OR, NOT, and NOR logic function. Furthermore, to illustrate AND, and NAND switching function using the foregoing switching function, which is implemented by the Petri net graph. The main purpose of the paper is to prove ours hypothesis that the most logic function can be represented by the Petri net graph. Ultimately, our assumptions are complemented trustily.     

Stochastic Petri net representation of discrete event simulations

In the context of discrete event simulation, the marking of a stochastic Petri net (SPN) corresponds to the state of the underlying stochastic process of the simulation and the firing of a transition corresponds to the occurrence of an event. A study is made of the modeling power of SPNs with timed and immediate transitions, showing that such Petri nets provide a general framework for simulation. The principle result is that for any (finite or) countable state GSMP (generalized semi-Markov process) there exists an SPN having a marking process that mimics the GSMP in the sense that the two processes (and their underlying general state-space Markov chains) have the same finite dimensional distributions     

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     

模糊空间Petri网的规则表示及动态推理

为便于表示模糊空间Petri网的状态变迁规则,根据空间关联影响区域分布现实特点,提出了空间模糊Petri网中的状态关联影响规则、变迁关联影响规则和多阈值激活规则。依据模糊产生式规则的特点,详细描述了10种具体的推理规则和表示组件,并以实例加以说明。在此基础上,结合模糊空间Petri网的特点提出了动态推理过程算法,可以实现各种空间状态规则因子的转化。动态推理的过程不仅可以获取某种“结果”,而且可以挖掘基于空间位置关联的中间状态及引起中间状态变化的事件,可以有效地指导风险过程预测和控制。     

应用带标识的模糊Petri网的知识表示方法

提出一种在某些库所中带有标识的模糊Petri网模型来进行知识表示。为了获得更多的加权模糊产生式规则的信息,在知识表示的过程中考虑了权值,确定性因子,阈值等参数。这种模糊Petri网充分利用了Petri网的并行处理能力。随着带标识的模糊Petri网的运行,网中标识的变化可以标记加权模糊推理的运行。通过文中给出的基于相似性测度的计算方法可以更加高效地计算出多层加权模糊推理的推理结果。     

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     

多值逻辑网络的输出跟踪牵制控制

本文利用代数状态空间方法,研究了多值逻辑控制网络的输出跟踪牵制控制.首先利用矩阵的半张量积给出了带牵制控制的多值逻辑控制网络的代数表示.其次基于该代数表示,定义了一组合适的能达集,并建立了多值逻辑控制网络输出跟踪牵制控制器的设计方法.再次,利用多值逻辑哑算子的性质,给出了多值逻辑控制网络分布式输出跟踪控制问题可解的充要条件.最后将所得的理论结果应用于网络演化博弈的演化行为分析.     

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.     

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     

On reachability graphs of Petri nets

Petri net is a powerful tool for system analysis and design. Several techniques have been developed for the analysis of Petri nets, such as reachability trees, matrix equations and reachability graphs. This article presents a novel approach to constructing a reachability graph, and discusses the application of the reachability graph to Petri nets analysis.     

A generalized fuzzy Petri net model

The paper proposes a new model of Petri nets based on the use of logic based neurons. In contrast to the existing generalizations, this approach is aimed at neural-type modeling of the entire concept with a full exploitation of the learning capabilities of the processing units being used there. The places and transitions of the net are represented by OR and AND-type and DOMINANCE neurons, respectively. A correspondence between this model and the previous two-valued counterpart is also revealed. The learning aspects associated with the nets are investigated     

微分Petri网的稳定性分析

针对混合系统的特点,建立其微分Petri网（DPN）的模型．首先,给出一类DPN的稳定性概念和稳定性引理;然后通过引入两类函数,利用关联矩阵的信息对DPN的稳定性进行具体分析,进而构造新的复合能量函数,得到DPN的稳定性定理;最后通过仿真例子说明定理的有效性．     

面向对象Petri网建模技术综述

阐述了面向对象技术和Petri网的结合方式,提出了面向对象Petri网的建模过程,给出其详细的建模步骤和流程图,讨论了面向对象Petri网的动态特性分析方法,分析和总结了OOPN,OOCPN、OOAPN以及OOTPN的研究现状和各自建模的利弊,最后对面向对象Petri网的相关技术和发展趋势进行了综述与展望.