Statechartable Petri nets

Petri nets and statecharts can model concurrent systems in a succinct way. While translations from statecharts to Petri nets exist, a well-defined translation from Petri nets to statecharts is lacking. Such a translation should map an input net to a corresponding statechart, having a structure and behaviour similar to that of the input net. Since statecharts can only model a restricted form of concurrency, not every Petri net has a corresponding statechart. We identify a class of Petri nets, called statechartable nets, that can be translated to corresponding statecharts. Statechartable Petri nets are structurally defined using the novel notion of an area. We also define a structural translation that maps each statechartable Petri net to a corresponding statechart. The translation is proven sound and complete for statechartable Petri nets.     

Compositional semantics of a real-time prototyping language

The formal semantics of a prototyping language for hard real-time systems, PSDL, is given. PSDL provides a data flow notation augmented by application-orientation timing and control constraints to describe a system as a hierarchy of networks of processing units communicating via data streams. The semantics of PSDL are defined in terms of algebraic high-level Petri nets. This formalism combines algebraic specifications of abstract data types with process and concurrency concepts of Petri nets. Its data abstraction facilities are used to define the meaning of PSDL data types, while high-level Petri nets serve to model the casual and timing behavior of a system. The net model exposes potential concurrency of computation and makes all synchronization needs implied by timing and control constraints explicit and precise. Time is treated as state of clocks, and clocks are modeled as ordinary system components. The net semantics provides the basis for applying analysis techniques and semantic tools available for high-level Petri nets     

Compositional Petri Net Approach to the Development of Concurrent and Distributed Systems

In the paper, a formal model based on Petri nets is proposed in the context of a compositional approach to the development and analysis of complex concurrent and distributed systems. Mutlilabels of Petri nets are introduced allowing labeling a transition not only with a single symbol, but also with a multiset of symbols. Operations on multilabeled Petri nets—parallel composition and restriction—are defined. A definition of a Petri net entity is given based on the notion of multilabels. A Petri net entity is a Petri net with a set of multilabels, where each multilabel is regarded as an access point of the entity. The operation of entity composition is introduced. Equivalence of entities is defined based on bisimulation equivalence of Petri nets. It is shown that the equivalence relation is congruent with respect to entity composition. It is also demonstrated that the composition operation is commutative and associative.     

T-组合Petri网的活性和公平性分析

同步合成是研究复杂Ｐｅｔｒｉ网系统性质的有效途径．文中通过引入可引发变迁序偶的概念,研究了Ｔ－组合（同步合成）Ｐｅｔｒｉ网对子网的活性和公平性继承关系,给出了一组Ｔ－组合Ｐｅｔｒｉ网活或公平的充要条件和充分条件．这些结果对网组合同步设计具有重要的指导意义     

“Truly concurrent” and nondeterministic semantics of discrete-time Petri nets

In the paper, a “truly concurrent” and nondeterministic semantics is defined in terms of branching processes of discrete-time Petri nets (DTPNs). These nets may involve infinite numbers of transitions and places, infinite number of tokens in places, and (maximal) steps of concurrent transitions, which allows us to consider this class of DTPNs to be the most powerful class of Petri nets. It is proved that the unfolding (maximal branching process) of the DTPN is the greatest element of a complete lattice constructed on branching processes of DTPNs with step semantics. Moreover, it is shown that this result is true also in the case of maximal transition steps if additional restrictions are imposed on the structure and behavior of the DTPN.     

Two polygraphic presentations of Petri nets

This document gives an algebraic and two polygraphic translations of Petri nets, all three providing an easier way to describe reductions and to identify some of them. The first one sees places as generators of a commutative monoid and transitions as rewriting rules on it: this setting is totally equivalent to Petri nets, but lacks any graphical intuition. The second one considers places as one-dimensional cells and transitions as two-dimensional ones: this translation recovers a graphical meaning but raises many difficulties since it uses explicit permutations. Finally, the third translation sees places as degenerated two-dimensional cells and transitions as three-dimensional ones: this is a setting equivalent to Petri nets, equipped with a graphical interpretation.     

共享路径合成网的活性和公平性分析

本文提出了Ｐｅｔｒｉ网的共享路径合成网的概念,研究了合成网对子网的活性和公平性继承关系,最后给出一种实现共享路径合成网活性和公平性的控制装置,这些结果为网系统合成提供了有力手段,并对发系统的相关性质分析有重要的应用价值。     

An equivalence theorem for labeled marked graphs

Petri nets and their languages are a useful model of systems exhibiting concurrent behavior. The sequential language associated with a given Petri net S consists of all possible firing sequences of S, where each element of a firing sequence is a single transition. The concurrent language associated with S consists of all possible concurrent firing sequences of S, where each element of a concurrent firing sequence is a set of transitions. The sequential language and the concurrent language associated with S are denoted by (L)(S) and (π)(S), respectively. In this paper, we consider an important special ease of Petri nets, called labeled marked graphs. The main result derived in this paper states that if Γ₁ and Γ₂ are two structurally deterministic labeled marked graphs, then (L)(Γ₁)=L(Γ₂)&rlhar2;π(Γ ₁)=π(Γ₂)     

模糊Petri网在带权不精确知识表示和推理中的应用研究

Petri网是一种适合于描述异步并发事件的计算机系统模型 ,可以有效地对并行和并发系统进行形式化验证和行为分析 .以模糊 Petri网的基本定义为基础 ,讨论了带权模糊知识的模糊产生式系统表示法 ,建立了这种表示法与模糊 Petri网之间的映射关系和转换算法 ;在对模糊 Petri网进一步扩充的基础上 ,解决了与知识的模糊Petri网表示相关的几个问题 ;最后给出了模糊 Petri网中不确定性的计算方法和相应的不精确推理算法     

Concurrent bisimulations in Petri nets

Summary After various attempts, an equivalence relation is defined for labelled Petri nets, on the base of the concurrency semantics of net theory. This relation, called Fully Concurrent bisimulation and abbreviated FC-bisimulation, preserves the level of concurrency of visible operations and, under some conditions, allows to enforce injective labelling on them. Refinements of a visible operation are also defined and we show that, under some conditions, they preserve FC-bisimulation.Research partly supported by ESPRIT Basic Research Action, project 3148: DEMON     

A computer network based control architecture for autonomous distributed multirobot systems

This paper presents the specification and implementation procedure using a microcomputer network based autonomous distributed control architecture for industrial multirobot systems. The procedure is based on the concept of data flow network controlled by communicating sequential processes to perform coordinated tasks. Robots and other computerized industrial devices such as conveyors and manufacturing machines are defined as object-oriented Petri nets. A modular and hierarchical approach is adopted to define a set of Petri net type diagrams which represent concurrent activities of control processes for such devices. Asynchronous and synchronous interactions are modelled by places and transitions, respectively, in global process interaction nets. The control software is implemented on a computer network using Inmos transputers with true parallel processing and message passing primitives efficiently handled in hardware. Petri net based models are directly and efficiently transformed to corresponding codes in occam, the high level parallel programming language defined for the transputer.     

Symbolic execution of concurrent systems using Petri nets

Techniques for analyzing sequential programs in order to improve their reliability have been widely studied in the past. Among the most interesting analysis techniques, we consider symbolic execution. However, analysis techniques for concurrent programs, and in particular symbolic execution, are still an open research area. In this paper, we define a method for symbolic execution of concurrent systems, based on an extension of the Petri net formalism, called EF nets. EF nets are a powerful, highly expressive and general formalism. Depending on the level of abstraction of actions and predicates that one associates to the transitions of the net, EF nets can be used as a high-level specification formalism for concurrent systems, or as a lower level internal representation of concurrent programs. Thus, the model is not dependent on a particular concurrent programming language, but it is flexible enough to be the kernel model for the representation of a wide set of systems and programming languages. In the paper, in order to support the analysis of a concurrent system or program, at first a general algorithm for symbolically executing an EF net is defined. Then, a more efficient algorithm is given for the particular, though important, subclass of EF nets, defined as safe EF nets. Such algorithm is proved to significantly help in reducing the amount of information needed to characterize a symbolic execution. Both the modelling power of the EF nets and the usefulness of the concurrent symbolic execution algorithms defined are illustrated by means of a case study.     

Extending Petri nets for specifying man–machine dialogues

The requirements of man-machine dialogue-specification techniques are examined. Petri nets are identified as possible candidates for a modelling technique for dialogues on the basis of their applicability to concurrent, asynchronous systems. Labelled Petri nets are extended to nested Petri nets, allowing transitions to invoke subnets. It is shown that this extension allows nested Petri nets to generate at least the set of context-free languages. Further extensions are made to simplify the modelling of input and output in the user interface, resulting in input-output nets. Transitions labelled by error conditions and meta functions on nets are introduced to increase the usability of the model. Finally, the use of the model is demonstrated by modelling a small hypothetical command language.     

M-nets: An algebra of high-level Petri nets, with an application to the semantics of concurrent programming languages

This paper describes a high-level Petri net model called M-nets (for modular multilabelled nets). A distinctive feature of this model is that it allows both: unfolding, as do most other high-level net models; and composition – in particular, synchronisation – in a process algebraic style, turning the set of M-nets into an algebraic domain. It turns out that the composition operations of this domain have various algebraic properties. Moreover, the model is such that composition operations are coherent with unfolding, in the sense that the unfolding of a composite high-level net is the composition of the unfoldings of its components. One of the motivations for M-nets is that they be a vehicle for giving semantics of concurrent programming languages. To illustrate their capability for that, the compositional semantics of – a simple, expressive concurrent programming language – is given. An associated low-level net semantics is described, and the coherence of these high-level and low-level semantics is proved. Received: 20 November 1996 / 13 January 1998     

UML2.0顺序图的形式化研究

在UML2.0规范中顺序图的语义仍然是以自然语言的形式描述的,为实现对顺序图的自动化分析和验证,必须为顺序图定义一种形式化的语义模型.为此首先给出了UML顺序图的一种符合BNF范式的形式化语法,然后为该语法中的非终止符定义转换规则,将UML顺序图中的基本动作转换为加标Petri网组件,最后定义了各种合成操作,利用这些合成操作可以将UML顺序图的加标Petri网组件转换为加标Petni网.     

Data and time abstraction techniques for analyzing multilevelconcurrent systems

It is argued that the design and analysis of a concurrent system can be made simpler and more intuitive if execution times of abstract operations are arbitrarily but systematically defined. This technique (time abstraction) is complementary to data abstraction and is more effective when used in combination with data abstraction. As examples, a bounced-buffer monitor and a multilevel concurrency scheme for a database system are analyzed by using data and time abstraction     

基于资源配置混杂Petri网的混杂系统生产过程建模

为了增强混杂Ｐｅｔｒｉ网解决资源共享和资源冲突的能力,定义一种新的混杂Ｐｅｔｒｉ网模型———资源配置混杂Ｐｅｔｒｉ网,提出了相应的使能和激发规则．将对连续变迁和离散变迁的控制作用引入混杂Ｐｅｔｒｉ网,同时,增加了资源配置变迁和资源释放变迁,用于有效分配可重复利用的资源．以典型的混杂生产过程为例,研究混杂系统生产过程建模．研究结果表明,所定义的模型描述能力强,模型语义正确合理,能够有效描述和分析混杂系统生产过程．     

Algebraic approaches for fault identification in discrete-event systems

In this note, we develop algebraic approaches for fault identification in discrete-event systems that are described by Petri nets. We consider faults in both Petri net transitions and places, and assume that system events are not directly observable but that the system state is periodically observable. The particular methodology we explore incorporates redundancy into a given Petri net in a way that enables fault detection and identification to be performed efficiently using algebraic decoding techniques. The guiding principle in adding redundancy is to keep the number of additional Petri net places small while retaining enough information to be able to systematically detect and identify faults when the system state becomes available. The end result is a redundant Petri net embedding that uses 2k additional places and enables the simultaneous identification of 2k-1 transition faults and k place faults (that may occur at various instants during the operation of the Petri net). The proposed identification scheme has worst-case complexity of O(k(m+n)) operations where m and n are respectively the number of transitions and places in the given Petri net.     

Using flat concurrent Prolog in system modeling

The flat concurrent Prolog (FCP) language, which enables the implementation of synchronization through data flow, communication through shared variables, parallelism through the reduction of the AND components in the clause's body, and indeterminacy through guarded commands, is discussed. It is shown that FCP, used in conjunction with Petri net methods, forms a powerful tool in the modeling of parallel systems that involve concurrency. The simulation of systems represented by various types of Petri nets is achieved using the reduction process of FCP. AND parallelism supports free competition among conflicting enabled transitions. A structural analysis of systems is provided using the metaprogramming technique     

Petri nets, algebras, morphisms, and compositionality

It is shown how a category of Petri nets can be viewed as a subcategory of two sorted algebras over multisets. This casts Petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition—the morphisms here respect the behaviour of nets. The categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components; for example, various forms of parallel composition of Petri nets arise naturally from the product in the category. This abstract setting makes plain a useful functor from the category of Petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of Petri nets—for instance, the coloured and higher level nets of Kurt Jensen arise through a simple modification of the sorts of the algebras underlying nets. Further, it provides a smooth formal relation with other models of concurrency such as Milner's calculus of communicating systems (CCS) and Hoare's communicating sequential processes (CSP), though this is only indicated in this paper.