Priority conflict-free Petri nets

A number of problems concerning priority conflict-free Petri nets are investigated in this paper. We show the reachability problem for such Petri nets to be NP-complete. (Using a similar technique, the NP-completeness result applies to the class of priority BPP-nets as well.) As for the boundedness problem, an NP-completeness result is demonstrated for priority conflict-free Petri nets with two types of prioritized transitions. (In contrast, the problem is known to be P-complete for conflict-free Petri nets without priorities.) We also investigate the home state problem, i.e., the problem of determining whether home states exist in a given a Petri net, for conflict-free Petri nets with and without priorities. As it turns out, home states always exist for bounded conflict-free Petri nets without priorities. If an additional liveness constraint is imposed, such Petri nets are guaranteed to be ‘reversible’ (i.e., their initial states are home states). For priority conflict-free Petri nets, being bounded and live is sufficient for the existence of home states. However, if the liveness assumption is dropped, the existence of home states is no longer guaranteed. Received: 1 April 1997 / 8 December 1997     

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.     

Bounds on the Number of Markings Consistent With Label Observations in Petri Nets

In this paper, we consider state estimation in discrete-event systems (DESs) modeled by labeled Petri nets and present upper bounds on the number of system states (or markings) that are consistent with an observed sequence of labels. Our analysis is applicable to Petri nets that may have nondeterministic transitions (i.e., transitions that share the same label) and/or unobservable transitions (i.e., transitions that are associated with the null label). More specifically, given knowledge of a labeled Petri net structure and its initial state, we show that the number of consistent markings in a Petri net with nondeterministic transitions is at most polynomial in the length of the observation sequence (i.e., polynomial in the number of labels observed). This polynomial dependency of the number of consistent markings on the length of the observation sequence also applies to Petri nets with unobservable transitions under the assumption that their unobservable subnets are structurally bounded. The bounds on the number of markings established in this paper imply that the state estimation problem in labeled Petri nets can be solved with complexity that is polynomial in the length of the observation sequence.     

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.     

基于Petri网语言的并发系统性质研究

给出Petri网弱活性（无死锁）与活性的两个语言刻画,讨论了同步合成Petri网的语言性质,基于Petri网语言,给出了判定Petri网活性的充分必要条件。同时研究了Petri网同步合成过程中活性保持问题,给出保持活性的充分必要条件。这些结果为讨论网的活性测试和控制提供了形式语言的方法。     

带抑制弧Petri网的保性变换

Petri 网的保性化简是Petri网分析的一种重要途径。带抑制弧的增广Petri网在计算能力上与图灵机等价。针对带抑制的增广Petri网中串联变迁和串联库所两类情况进行了较深入的分析,在给出了相关化简方法的基础上,证明了通过这些化简规则所得到的网系统与原网在活性、有界性、弱公平性等动态性质上仍保持一致。     

Can I find a partner? Undecidability of partner existence for open nets

We study open nets as Petri net models of web services, with a link to the practically relevant language WS-BPEL. For those nets, we investigate the problem of operability which we consider as fundamental as the successful notion of soundness for workflow nets, i.e., Petri net models of business processes and workflows. While we could give algorithmic solutions to the operability problem for subclasses of open nets in earlier work, this article shows that the problem is in general undecidable.     

Discrete-event models of a railway network

This paper constructs discrete-event models for the basic elements of railway networks, i.e., a station-to-station block with a passing track, a segment (as a part of a station-tostation block), a segment section (a block section), a railway point, as well as train operation models. All models represent Petri nets with bounding arcs. The group control of the models under the parallel-conveyor movements of trains is implemented by special control elements (the so-called supervisors) that ensure railway traffic safety requirements.     

Reduction rules for reset/inhibitor nets

Reset/inhibitor nets are Petri nets extended with reset arcs and inhibitor arcs. These extensions can be used to model cancellation and blocking. A reset arc allows a transition to remove all tokens from a certain place when the transition fires. An inhibitor arc can stop a transition from being enabled if the place contains one or more tokens. While reset/inhibitor nets increase the expressive power of Petri nets, they also result in increased complexity of analysis techniques. One way of speeding up Petri net analysis is to apply reduction rules. Unfortunately, many of the rules defined for classical Petri nets do not hold in the presence of reset and/or inhibitor arcs. Moreover, new rules can be added. This is the first paper systematically presenting a comprehensive set of reduction rules for reset/inhibitor nets. These rules are liveness and boundedness preserving and are able to dramatically reduce models and their state spaces. It can be observed that most of the modeling languages used in practice have features related to cancellation and blocking. Therefore, this work is highly relevant for all kinds of application areas where analysis is currently intractable.     

Modular nets of active resources

Nets of active resources (AR nets) make up the dual syntax of Petri nets, in which places and transitions are combined into a general set of nodes, whereas a set of arcs, vice versa, is decomposed onto disjoint sets of consuming and producing arcs. Contrary to Petri nets, the object (token) in the AR nets can be considered as the passive and active agent simultaneously. It is shown that the uniform structure of the AR nets’ nodes provides new possibilities of modular simulation of systems. Different types of modules and ways of decomposition onto modules in the AR nets, as well as the properties of the equivalent replacements of modules, are investigated.     

Trace- and failure-based semantics for responsiveness

We study open systems modeled as Petri nets with an interface for asynchronous (i.e., buffered) communication with other open systems. As a minimal requirement for successful communication, we investigate responsiveness, which guarantees that an open system and its environment always have the possibility to communicate. We investigate responsiveness with and without final states and also their respective bounded variants, where the number of pending messages never exceeds a previously known bound. Responsiveness accordance describes when one open system can be safely replaced by another open system. We present a trace-based characterization for each accordance variant. As none of the relations turns out to be compositional (i.e., it is no precongruence), we characterize the coarsest compositional relation (i.e., the coarsest precongruence) that is contained in each relation, using a variation of should testing. For the two unbounded variants, the precongruences are not decidable, but for the two bounded variants we show decidability.     

Verifying time Petri nets by linear programming

The paper proposes an approach to solving some verification problems of time petri nets using linear programming.The approach is based on the observation that for loop-closed time Ptri nets,it is only necessary to investigate a finite prefix of an untimed run of the underlying Petri net.Using the technique the paper gives solutions to reachabiltiy and bounded delay timing analysis problems.For both problems algorithms are given,that are decision procedures for loop-closed time Petri nets.and semi-decision procedures for general time Petri nets.     

柔性制造系统非阻塞监督控制器优化设计

针对一类含有并发执行装配过程的柔性制造系统G-systems,提出一种新的死锁预防策略保证该系统的非阻塞性,即在控制下,受控系统从任意可达状态都可以到达理想状态.首先对Petri网模型中基本信标实施控制,保证了基本信标的最大可控,然后通过线性规划算法求取所有从属信标满足可控性的条件,即获得基本信标的控制深度变量.与现有方法相比,该策略优点在于只需加入少量的控制库所,就可避免不必要的迭代过程;其次是提出控制器输出弧位置优化策略,得到了结构更为简单、许可行为更多的非阻塞Petri网控制器.     

基于Petri网模型的随机数生成器

以连续Petri网概念为基础,引入带弧权和禁止弧的扩展连续Petri网,将扩展连续Petri网作为工具对随机数生成器进行研究。选用随机数学中的乘同余法产生服从[0,1]均匀分布的随机变量,从而解决Petri网的规模因随机变量的精度增加而急剧增大的问题,针对某些逆变换法无法实现的分布,引入拒绝法,对现有的随机数发生器Petri网模型进行改进。     

Relating SPO and DPO graph rewriting with Petri nets having read, inhibitor and reset arcs

It belongs to the folklore that graph grammars can be seen as a proper generalisation of Petri nets. In this paper we show how this intuitive relationship can be made formal. The double-pushout approach to graph rewriting turns out to be strictly related to Petri nets with read and inhibitor arcs, while the single-pushout approach has strong connections to Petri nets with read and reset arcs.     

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.     

Framework for modeling and analysis of distributed problem-solving systems

Petri nets have the basic concepts necessary to model distributed systems with asynchronous processes. Petri nets are not directly applicable to certain kinds of systems like distributed intelligent systems (DISs). These are complex systems where multiple intelligent agents cooperate through communication to achieve the solution to a problem. The paper identifies the limitations of ordinary Petri nets for modeling DISs and proposes extensions. The extended Petri net incorporates colored tokens, inhibition arcs, non-primitive places and transitions, multiple copies of tokens and cumulative places. It is called a distributed problem-solving Petri net. The definitions and analysis techniques are given and illustrated by means of an example.