Abstract processes of place/transition systems

A well-known problem in Petri net theory is to formalise an appropriate causality-based concept of process or run for place/transition systems. The so-called individual token interpretation, where tokens are distinguished according to their causal history, giving rise to the processes of Goltz and Reisig, is often considered too detailed. The problem of defining a fully satisfying more abstract concept of process for general place/transition systems has so-far not been solved. In this paper, we recall the proposal of defining an abstract notion of process, here called BD-process, in terms of equivalence classes of Goltz-Reisig processes, using an equivalence proposed by Best and Devillers. It yields a fully satisfying solution for at least all one-safe nets. However, for certain nets which intuitively have different conflicting behaviours, it yields only one maximal abstract process. Here we identify a class of place/transition systems, called structural conflict nets, where conflict and concurrency due to token multiplicity are clearly separated. We show that, in the case of structural conflict nets, the equivalence proposed by Best and Devillers yields a unique maximal abstract process only for conflict-free nets. Thereby BD-processes constitute a simple and fully satisfying solution in the class of structural conflict nets.     

Configuration structures, event structures and Petri nets

In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without self-loops, under the collective token interpretation. To this end we propose a more general form of event structure, matching the expressive power of such nets. These new event structures and nets are connected by relating both notions with configuration structures, which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them, but abstract from any auxiliary structure.A configuration structure can also be considered logically, as a class of propositional models, or—equivalently—as a propositional theory in disjunctive normal from. Converting this theory to conjunctive normal form is the key idea in the translation of such a structure into a net.For a variety of classes of event structures we characterise the associated classes of configuration structures in terms of their closure properties, as well as in terms of the axiomatisability of the associated propositional theories by formulae of simple prescribed forms, and in terms of structural properties of the associated Petri nets.     

A Petri net model for integrated process and job shop production planning

In this paper a new Petri net class (Chameleon systems) for modeling and analyzing joined process planning and job shop production planning is proposed based on the multi-level Petri net model introduced by Valk (1995). Chameleon system is a High-level Petri net extended with time that consists of a High-level Petri net modeling the workshop which is called system net and ordinary Petri net modeling the jobs and setups which act as tokens of the system net and therefore are called token nets. Process plans of the jobs are partial orders of operation groups and alternatives. The uncertainty of operation duration is captured by a new time model. The advantages of this new modeling approach are the following: (i) a modular construction of the joined process and job shop planning is allowed, (ii) classical known Petri net analysis methods can be applied and (iii) the analysis can be done at different levels of abstraction.     

Complexity of some problems in Petri nets

We consider the complexity of several standard problems for various classes of Petri nets. In particular, the reachability problem, the liveness problem and the k-boundedness problems are analyzed. Some polynomial time and polynomial space complete problems for Petri nets are given. We then show that the problem of deciding whether a Petri net is persistent is reducible to reachability, partially answering a question of Keller. Reachability and boundedness are proved to be undecidable for the Time Petri net introduced by Merlin. Also presented is the concept of controllability, i.e., the capability of a set of transitions to disable a given transition. We show that the controllability problem requires exponential space, even for 1-bounded nets.     

Verification of causal models using petri nets

Many different approaches, mainly based on logical formalisms, have been proposed for modeling causal knowledge and the inferential mechanisms based on this type of knowledge. In this article we present an alternative approach to this problem in which the semantics of a causal model is provided by adopting Petri nets. We show how this scheme of modeling is powerful enough to capture all crucial aspects of the corresponding causal model, without resorting to very complex structures; indeed, the model is obtained using a particular type of deterministic Petri net. Moreover, a complete formalization of the aspects concerning the correctness of the represented causal model is provided in terms of reachability in the Petri net. We believe that this aspect is very important in the knowledge acquisition phase when precise correctness criteria should be defined and respected in the construction of the model. We analyze some of these criteria and we discuss an algorithm (based on a backward simulation of the net) capable of discovering incorrectness by exploiting analysis tools available for Petri nets and the explicit parallelism of the model. © 1992 John Wiley & Sons, Inc.     

Toward the use of Petri nets for the formalization of OWL-S choreographies

In this paper, we present a Petri net-based approach for modeling the choreography of semantic Web services which are described following the OWL-S specification. In our approach, each control construct of the OWL-S choreography is represented through a Petri net pattern that captures formally its operational semantics. The main difference between our work and the main proposals that model the semantics of OWL-S services choreography is that, although both approaches represent the service choreography with Petri nets, our proposal is also concerned with the practical execution of the Petri nets by the client. Therefore we also represent the flow of data, the outputs transformations, the effects in the environment, in addition to the structures that control the choreography of the services in our Petri net models. The implementation of the OWL-S choreography is performed in a Petri net ontology-based engine. This is another difference with traditional approaches that only use Petri nets for the analysis of the service properties. Furthermore, the use of an underlying ontology engine for supporting both the domain models of OWL-S services and the Petri net models provides several advantages in terms of reasoning, extension, and reuse.     

基于Petri网的柔性制造系统一种预防死锁方法

基于Petri网的结构特性分析,研究了FMS(柔性制造系统)一种预防死锁方法.提出了 Petri网的一种特殊拓扑结构--基本信标的概念.在Petri网中基本信标的集合是SMS(严格极 小信标)集合的一个真子集.尤其在大型Petri网系统中,基本信标的集合比SMS的集合要小得 多.对于Petri网的一个子类S3PR,只对每一个基本信标添加一个库所使其不被清空,就可实现 预防死锁,也就是说无须控制S3PR的所有SMS而达到无信标被清空的目的.此外,对于S3PR, 还提出了一种求取SMS和基本信标的方法.相对于现在普遍采用的控制所有SMS来预防死锁 的策略,其具三方面优势.1)只需控制少量的SMS即所谓的基本信标.相应地,添加少量的控制 库所和连接弧,就可得到无死锁或活的Petri网.2)不需要先行计算出极小信标的集合.3)明显 地,这种方法更适合大型Petri网系统.我们通过穿插在文中的一个例子来说明这些方法.     

Two theoretical and practical aspects of knitting technique:invariants and a new class of Petri net

We present two aspects of knitting technique, the structural properties (especially the P- and T-invariants), and the synchronized choice net (a new class of Petri net), that are of both theoretical importance and practical uses to the verification of structural correctness of a Petri net or to detect the structural problem of a Petri net. This work first proves that the ordinary Petri nets synthesized with knitting technique are structurally bounded, consistent, conservative and safe (when each home place holds one token) using the well-known linear algebra approach. It also provides a procedure for finding P- and T-invariants for Petri net synthesized using the knitting technique. We present examples for P-invariants and show that we can synthesize Petri nets more general than the "asymmetric-choice nets". The algorithm for finding P-invariants of ordinary Petri nets is extended to find the P-invariants for a general Petri net synthesized with knitting technique and the arc-ratio rules. We present a new class of Petri nets, called synchronized choice nets, which are the largest set of Petri nets that can be covered by both T-components and P-components. An algorithm is proposed to find its T-components and the P-components, respectively. The complexity of this algorithm is also presented. The theory of synchronized choice nets has the potential to simplify that for free choice nets.     

The synthesis problem of Petri nets

The synthesis problem of concurrent systems is the problem of synthesizing a concurrent system model from sequential observations. The paper studies the synthesis problem for elementary Petri nets and transition systems. A characterization of the class of transition systems which correspond to elementary Petri nets is proven. It is shown how to generate all elementary Petri nets corresponding to a given transition system. If there is any such elementary Petri net, it is proven that there always exists a small one which has only polynomially many elements in the size of the transition system. Received October 5, 1992 / April 11, 1995     

On the Regularity of Petri Net Languages

Petri nets are known to be useful for modeling concurrent systems. Once modeled by a Petri net, the behavior of a concurrent system can be characterized by the set of all executable transition sequences, which in turn can be viewed as a language over an alphabet of symbols corresponding to the transitions of the underlying Petri net. In this paper, we study the language issue of Petri nets from a computational complexity viewpoint. We analyze the complexity of theregularity problem(i.e., the problem of determining whether a given Petri net defines an irregular language or not) for a variety of classes of Petri nets, includingconflict-free,trap-circuit,normal,sinkless,extended trap-circuit,BPP, andgeneralPetri nets. (Extended trap-circuit Petri nets are trap-circuit Petri nets augmented with a specific type ofcircuits.) As it turns out, the complexities for these Petri net classes range from NL (nondeterministic logspace), PTIME (polynomial time), and NP (nondeterministic polynomial time), to EXPSPACE (exponential space). In the process of deriving the complexity results, we develop adecomposition approachwhich, we feel, is interesting in its own right, and might have other applications to the analysis of Petri nets as well. As a by-product, an NP upper bound of the reachability problem for the class of extended trap-circuit Petri nets (which properly contains that of trap-circuit (and hence, conflict-free) and BPP-nets, and is incomparable with that of normal and sinkless Petri nets) is derived.     

Extended Elementary Siphons and Their Application to Liveness‐Enforcement of Generalized Petri Nets

As a significant structural object, siphons are extensively employed to implement a large number of deadlock prevention and liveness‐enforcing methods for flexible manufacturing systems modeled by Petri nets. By linear combinations, a set of elementary siphons is chosen from all strict minimal ones to be controlled and thus the structural complexity of a supervisor is greatly reduced. The concept of elementary siphons is originally proposed for ordinary Petri nets. When applied to generalized Petri nets, their selection and controllability require an additional study. In this work, the concept of augmented siphons is proposed to extend the application of the elementary ones to a class of generalized Petri nets, GLS³PR. Based on graph theory, a siphon extraction algorithm is developed to obtain all strict minimal siphons, from which augmented elementary ones are computed. In addition, the controllability conditions of dependent siphons are developed. Through fully investigating the net structure, especially weight information, the set of augmented elementary siphons is more compact and well suits for generalized Petri net models under consideration. Some examples are used to illustrate the proposed method.     

Petri nets,event structures and domains,part I

The general aim of this paper is to find a theory of concurrency combining the approaches of Petri and Scott (and others).In part I we introduce our formalisms. To connect the abstract ideas of events and domains of information, we show how casual nets induce certain kinds of domains where the information points are certain sets of events. This allows translations between the languages of net theory and domain theory. Following the idea that events of causal nets are occurrences, we generalise causal nets to occurrence nets, by adding forwards conflict. Just as infinite flow charts unfold finite ones, so transition nets can be unfolded into occurrence nets. Next we extend the above connections between nets and domains to these new nets. Event structures which are intermediate between nets and domains play an important part in all our work. Finally, as an example of how concepts translate from one formalism to the other, we show how Petri's notion of confusion ties up with Kahn and Plotkin's concrete domains.In part II we shall continue the job of connecting up notions within net theory and the theory of domains. In particular, we shall examine the idea of states of computations.     

Determination of path identifiers for reliability analysis of a broadcasting network using Petri nets

A Petri net approach for determination of the sets of path identifiers for reliability analysis of a broadcasting network is presented. The firing concept of Petri nets is exploited to give a Petri net interpretation to certain properties of the network. The dynamic behaviour of the system under study is represented in the form of token movements within the model. The various entities of Petri nets are assigned an appropriate interpretation for studying the behaviour of the system at different levels. Corresponding to the source node and each of the terminal nodes, a vector, representing the state of the Petri net interpreted model, is defined by assuming a token initially at the source place and finally at one of the terminal places. The reachability and marking concepts are then used to determine all success states of the system. The developed algorithm has been coded into FORTRAN-77 and the complete package is available. The proposed technique is extremely simple as it uses only vector additions on the columns of the place-to-transition incident matrix.     

运输机器人行为建模的Petri网方法

针对建立运输机器人的精准行为模型所遇到的新困难,提出采用含禁止弧Petri网（PN）建立其行为模型。运输机器人行为有耦合、制约、异步等特点,采用含禁止弧的行为交互Petri网元模型以及token流动控制机制建模其行为。通过LabVIEW2012及Robotics模块,将Petri网模型转化为LabVIEW程序,在运输机器人平台进行行为验证。结果实现了运输机器人的行为与交互逻辑,具有行为辨识、决策与执行能力。验证了含禁止弧Petri网为运输机器人的行为建模提供了一种适用方法,建立的Petri网模型为运输机器人的相关行为设计提供模型参考。     

Decomposition of Petri nets

The problem of splitting any given Petri net into functional subnets is considered. The properties of functional subnets and sets that induce them are investigated. An algorithm of polynomial complexity is constructed for decomposition of nets.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 131–140, September–October 2004.     

Deciding a class of path formulas for conflict-free petri nets

The aim of this paper is to develop a unified approach for deriving complexity results for problems concerning conflict-free Petri nets. To do so, we first define a class of formulas for paths in Petri nets. We then show that answering the satisfiability problem for conflict-free Petri nets is tantamount to solving a system of linear inequalities (which is known to be in P). Since a wide spectrum of Petri net problems (including various fairness-related problems) can be reduced to the satisfiability problem in a straightforward manner, our approach offers an umbrella under which many Petri net problems for conflict-free Petri nets can be shown to be solvable in polynomial time. As a side-product, our analysis provides evidence as to why detecting unboundedness for conflict-free Petri nets is easier (provided P ≠ NP) than for normal and sinkless Petri nets (which are two classes that properly contain conflict-free Petri nets). A preliminary version was presented at the 14th International Conference on Application and Theory of Petri Nets, Chicago, IL, USA, June 1993.     

A technique of state space search based on unfolding

Unfoldings of Petri nets provide a method of searching the state space of concurrent systems without considering all possible interleavings of concurrent events. A procedure is given for constructing the unfolding of a Petri net, terminating the construction when it is sufficient to represent all reachable markings. This procedure is applied to hazard and deadlock detection in asynchronous circuits. Examples are given of scalable systems with exponential size state spaces, but polynomial size unfoldings, including a distributed mutual exclusion ring circuit.School of Computer Science, Carnegie Mellon University     

着色Petri网应用研究

着色Petri网是在经典Petri网理论基础上增加了token类型和网的模块这两个功能,它现在已成为一种较完善的语言,可以用来对各种系统规范和协议等进行设计、规范描写、仿真和验证等。文章对着色Petri网的基本理论进行了简单介绍,并对一个简单的通信协议进行建模和分析,提出了今后着色Petri网发展的一个主要方向。     

Well-structured languages

This paper introduces the notion of well-structured language. A well-structured language can be defined by a labelled well-structured transition system, equipped with an upward-closed set of accepting states. That peculiar class of transition systems has been extensively studied in the field of computer-aided verification, where it has direct an important applications. Petri nets, and their monotonic extensions (like Petri nets with non-blocking arcs or Petri nets with transfer arcs), for instance, are special subclasses of well-structured transition systems. We show that the class of well-structured languages enjoy several important closure properties. We propose several pumping lemmata that are applicable respectively to the whole class of well-structured languages and to the classes of languages recognized by Petri nets or Petri nets with non-blocking arcs. These pumping lemmata allow us to characterize the limits in the expressiveness of these classes of language. Furthermore, we exploit the pumping lemmata to strictly separate the expressive power of Petri nets, Petri nets with non-blocking arcs and Petri nets with transfer arcs.     

A Petri net model for probabilistic logic

In this article we investigate the use of Petri nets for the representation of possible worlds in probabilistic logic. We propose a method to generate possible worlds based upon the reachability tree of the Petri net model. The number of columns in the matrix of possible worlds grows exponentially with the problem size. Nilsson [Proceedings of 1976 National Computer Conference and Readings in Artificial Intelligence, Morgan Kaufmann, Los Altos, CA, 1981, pp. 192-199] suggested a method to generate only those columns of the possible world matrix that are likely to be important for the solution. We provide Petri net models for the method suggested by Nilsson and show that they lead to intuitive and simple computational methods. © 1996 John Wiley & Sons, Inc.