Showing papers on "Petri net published in 1996"

Coloured Petri nets (2nd ed.): basic concepts, analysis methods and practical use: volume 1

Abstract: This three-volume work presents a coherent description of the theoretical and practical aspects of coloured Petri nets. These CP-nets are shown to be a full-fledged language for the design, specification, simulation, validation and implementation of large software systems.The introductory first volume contains the formal definition of CP-nets and the mathematical theory behind their analysis methods. It gives a detailed presentation of many small examples and a brief overview of some industrial applications. The purpose of the book is to teach the reader how to construct CP-net models and analyse them by means of simulation. The book is also attractive to readers who are more interested in applications than in the underlying mathematics.

General decidability theorems for infinite-state systems

Abstract: Over the last few years there has been an increasing research effort directed towards the automatic verification of infinite state systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called well-structured systems), which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a well-ordered and well-founded preorder such that the transition relation is "monotonic" (is a simulation) with respect to the preorder. We show that the following properties are decidable for well-structured systems: reachability; eventuality; and simulation. We also describe how these general principles subsume several decidability results from the literature about timed automata, relational automata, Petri nets, and lossy channel systems.

An Improvement of McMillan's Unfolding Algorithm

Abstract: McMillan has recently proposed a new technique to avoid the state explosion problem in the verification of systems modelled with finite-state Petri nets. The technique requires to construct a finite initial part of the unfolding of the net. McMillan's algorithm for this task may yield initial parts that are larger than necessary (exponentially larger in the worst case). We present a refinement of the algorithm which overcomes this problem.

Deadlock avoidance policy for Petri-net modeling of flexible manufacturing systems with shared resources

Abstract: Multiple products through a flexible manufacturing system (FMS) with limited resources can lead to deadlock. In this paper, the authors study the problem of deadlock avoidance by using the Petri net (PN) model for FMSs and introducing the concept of deadlock structure. The necessary and sufficient conditions to prevent deadlock are characterized. The authors use a state feedback restriction policy which prevents some enabled transitions from firing for avoiding deadlock in the system. In particular, when the number of any key kind of resources is greater than one, this policy is minimally restrictive and allows the maximal use of resources in the system. The authors present the PN realization of these restriction policies when the closed-loop system can be modeled by a live PN. The restriction policies can be easily implemented. An example is provided for illustration.

Place or Transition Petri Nets

Abstract: This contributions provides an introduction to the theory of place/transition Petri nets Topics include the sequential and the concurrent behavior of place/ transition Petri nets, marking graphs and coverability trees, and some analysis techniques that are based on the structure of place/transition Petri nets

Graph processes

Abstract: We first give a new definition of graph grammars, which, although following the algebraic double-pushout approach, is more general than the classical one because of the use of a graph of types where all involved graphs are mapped to. Then, we develop a process-based semantics for such (typed) graph grammars, in the line of processes as normally used for providing a semantics to Petri nets. More precisely, we represent each equivalence class of derivations as a graph process, which can be seen as an acyclic graph grammar, plus a mapping of its items onto the items of the given grammar. Finally, we show that such processes represent exactly the equivalence classes of derivations up to the well-known shift-equivalence, which have always been used in the literature on graph grammars. Therefore graph processes are attractive alternative representatives for such classes. The advantage of dealing with graph processes instead of equivalence classes (or also representatives belonging to the equivalence classes) is that dependency and/or concurrency of derivation steps is explicitly represented.

Stochastic Petri Nets

Abstract: Will reading habit influence your life? Many say yes. Reading stochastic petri nets is a good habit; you can develop this habit to be such interesting way. Yeah, reading habit will not only make you have any favourite activity. It will be one of guidance of your life. When reading has become a habit, you will not make it as disturbing activities or as boring activity. You can gain many benefits and importances of reading.

Fluid stochastic petri nets: theory, applications, and solution

Abstract: In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.

An Introduction to the Practical Use of Coloured Petri Nets

Abstract: The development of Coloured Petri Nets (CP-nets or CPN) has been driven by the desire to develop a modelling language - at the same time theoretically well-founded and versatile enough to be used in practice for systems of the size and complexity found in typical industrial projects. To achieve this, we have combined the strength of Petri nets with the strength of programming languages. Petri nets provide the primitives for describing synchronisation of concurrent processes, while programming languages provide the primitives for definition of data types and manipulation of their data values.

On Liveness and Controlled Siphons in Petri Nets

Abstract: Structure theory of Petri nets investigates the relationship between the behavior and the structure of the net. Contrary to linear algebraic techniques, graph based techniques fully exploit the properties of the flow relation of the net (pre and post sets). Liveness of a Petri net is closely related to the validation of certain predicates on siphons. In this paper, we study thoroughly the connections between siphons structures and liveness. We define the controlled-siphon property that generalizes the well-known Commoner's property, since it involves both traps and invariants notions. We precise some structural conditions under which siphons cannot be controlled implying the structural non-liveness. These conditions based on local synchronization patterns cannot be captured by linear algebraic techniques. We establish a graph-theoretical characterization of the non-liveness under the controlled-siphon property. Finally, we prove that the controlled-siphon property is a necessary and sufficient liveness condition for simple nets and asymmetric choice nets. All these results are illustrated by significant examples taken from literature.

Hybrid Petri Nets: a

Abstract: The paper presents a model which provides a simple graphical representation of hybrid systems and takes advantage of the modular structure of Petri nets in giving a compact description of systems composed of interacting subsystems, both time-continuous and discrete-event. The modelling formalism seems rich enough to encompass large classes of hybrid systems and can easily represent many of the features of the models given in the literature.

Petri nets : a tool for design and management of manufacturing systems

Abstract: Basics of petri nets qualitative properties modelling of manufacturing systems - modelling and analysis of common modules modelling, analysis and optimization of cyclic manufacturing systems acyclic systems answers to exercises and problems.

The synthesis problem of Petri nets

Abstract: 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.

Functional descriptions used in computer support for qualitative scheme generation—“Schemebuilder”

Abstract: With increased pressures coming from global competition and requirements for greater innovation in product development, designers are hard pressed to deliver designs of higher quality and variety using a repertoire of technological options from different disciplines. This interdisciplinary product development approach has not only removed many of the traditional constraints to design but has now given designers a much wider freedom of choice as to the best solution to a design problem. The focus of this paper is a knowledge-based design environment called Schemebuilder, which is a comprehensive and integrated suite of software tools aimed at supporting the designer in the rapid development of product design models in the conceptual, through embodiment stages of design. Illustrated is the use of the software tools in the qualitative generation of alternative schemes, by application of stored working and decomposition principles in the development of a function-means tree-like information structure. With mechatronic product development as the main theme, this paper describes a closely integrated methodology that incorporates a bond graph approach to continuous-time energetic systems and high-level Petri nets for the rigorous description of discrete-time information systems. Additionally, a technique is suggested for the decomposition of free format statements of need into the rigorously defined design context and required functions, which form the starting point of the function-means development process.

Comparing models of computation

Abstract: We give a denotational framework (a meta model) within which certain properties of models of computation can be understood and compared. It describes concurrent processes as sets of possible behaviors. Compositions of processes are given as intersections of their behaviors. The interaction between processes is through signals, which are collections of events. Each event is a value-tag pair, where the tags can come from a partially ordered or totally ordered set. Timed models are where the set of tags is totally ordered. Synchronous events share the same tag, and synchronous signals contain events with the same set of tags. Synchronous systems contain synchronous signals. Strict causality (in timed systems) and continuity (in untimed systems) ensure determinacy under certain technical conditions. The framework is used to compare certain essential features of various models of computation, including Kahn process networks, dataflow, sequential processes, concurrent sequential processes with rendezvous, Petri nets, and discrete-event systems.

DYNAMITE: dynamic task nets for software process management

Abstract: Managing the software development and maintenance process has been identified as a great challenge for several years. Software processes are highly dynamic and can only rarely be planned completely in advance. Dynamic task nets take this into account. They are built and modified incrementally as a software process is executed. Dynamic task nets have been designed to solve important problems of process dynamics, deciding product-dependent structure evolution, feedback, and concurrent engineering. In order to describe editing and enactment (and their interaction) in a uniform way, task nets are formally defined by means of a programmed graph rewriting system.

Petri net models of flexible and automated manufacturing systems : a survey

Abstract: Petri nets (PNs) have recently emerged as a promising approach for modelling flexible and automated manufacturing systems. PNs are a graphical and mathematical modelling technique that is useful for modelling concurrent, asynchronous, distributed, parallel, nondeterministic, and stochastic systems, as attested by a steady stream of papers which appeared throughout the 1980s. Since 1989, there has been an explosion of interest in using PNs to model, simulate, and analyse manufacturing systems. We present an overview of PN theory. We then present a schema for categorizing PN models of manufacturing systems, followed by a survey of PN models of flow lines, automatic transfer lines, job shops, flexible manufacturing systems, and assembly systems. This discussion represents the most comprehensive survey of applications of PNs to manufacturing through 1994. Finally, we present a summary and some conclusions.

Decidability and Complexity of Petri Net Problems - An Introduction

Abstract: A collection of 10 “rules of thumb” is presented that helps to determine the decidability and complexity of a large number of Petri net problems.

A reasoning algorithm for high-level fuzzy Petri nets

Abstract: We introduce an automated procedure for extracting information from knowledge bases that contain fuzzy production rules. The knowledge bases considered here are modeled using the high-level fuzzy Petri nets proposed by the authors in the past. Extensions to the high-level fuzzy Petri net model are given to include the representation of partial sources of information. The case of rules with more than one variable in the consequent is also discussed. A reasoning algorithm based on the high-level fuzzy Petri net model is presented. The algorithm consists of the extraction of a subnet and an evaluation process. In the evaluation process, several fuzzy inference methods can be applied. The proposed algorithm is similar to another procedure suggested by Yager (1983), with advantages concerning the knowledge-base searching when gathering the relevant information to answer a particular kind of query.

Petri Nets and Other Models of Concurrency

Abstract: This paper retraces, collects, and summarises contributions of the authors — in collaboration with others — on the theme of Petri nets and their categorical relationships to other models of concurrency.

Grammar-based music composition

Abstract: L-Systems have traditionally been used as a popular method for the modelling of spacefilling curves, biological systems and morphogenesis. In this paper, we adapt string rewriting grammars based on L-Systems into a system for music composition. Representation of pitch, duration and timbre are encoded as grammar symbols, upon which a series of re-writing rules are applied. Parametric extensions to the grammar allow the specification of continuous data for the purposes of modulation and control. Such continuous data is also under control of the grammar. Using non-deterministic grammars with context sensitivity allows the simulation of Nth-order Markov models with a more economical representation than transition matrices and greater flexibility than previous composition models based on finite state automata or Petri nets. Using symbols in the grammar to represent relationships between notes, (rather than absolute notes) in combination with a hierarchical grammar representation, permits the emergence of complex music compositions from a relatively simple grammars.

Modeling logical and temporal synchronization in hypermedia systems

Abstract: The paper introduces a unified formal model for the complete and accurate specification of both temporal and logical (i.e., link) synchronization within hypermedia distributed and weakly synchronous systems. This new model extends time Petri nets with hierarchical design capabilities and new firing rules. These new firing rules enlighten the notion of hypermedia synchronization through powerful combinations of temporal and logical synchronization. Moreover, the proposed model offers an easy and concise modeling technique of asynchronous events in hypermedia systems.

On the use of kronecker operators for the solution of generalized stochastic petri nets

Abstract: We discuss how to describe the Markov chain underlying a generalized stochastic Petri net using Kronecker operators on smaller matrices. We extend previous approaches by allowing both an extensive type of marking-dependent behavior for the transitions and the presence of immediate synchronizations. The derivation of the results is thoroughly formalized, including the use of Kronecker operators in the treatment of the vanishing markings and the computation of impulse-based reward measures. We use our techniques to analyze a model whose solution using conventional methods would fail because of the state-space explosion. In the conclusion, we point out ideas to parallelize our approach.

Compositional Specification of Timed Systems (Extended Abstract)

Abstract: We present timed automata and timed Petri nets and argue that timed automata and their associated parallel composition operator are not well adapted for the compositional description of timed Petri nets. Timed automata with deadlines are presented. We present a compositional translation method from 1-safe timed Petri nets to this model. We also present basic ideas for a general compositional specification framework

Coloured Petri Nets - Basic Concepts, Analysis Methods and Practical Use - Volume 1, Second Edition

Abstract: Coloured Petri Nets-Kurt Jensen 2010-10-19 This book presents a coherent description of the theoretical and practical aspects of Coloured Petri Nets (CP-nets or CPN). It shows how CP-nets have been de veloped from being a promising theoretical model to being a full-fledged lan guage for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and/or com puters communicate by means of some more or less formal rules). The book contains the formal definition of CP-nets and the mathematical theory behind their analysis methods. However, it has been the intention to write the book in such a way that it also becomes attractive to readers who are more interested in applications than the underlying mathematics. This means that a large part of the book is written in a style which is closer to an engineering textbook (or a users' manual) than it is to a typical textbook in theoretical computer science. The book consists of three separate volumes. The first volume defines the net model (i. e. , hierarchical CP-nets) and the basic concepts (e. g. , the different behavioural properties such as deadlocks, fair ness and home markings). It gives a detailed presentation of many small exam ples and a brief overview of some industrial applications. It introduces the for mal analysis methods. Finally, it contains a description of a set of CPN tools which support the practical use of CP-nets.

Condensed state spaces for symmetrical coloured Petri nets

Abstract: This paper deals with state spaces. A state space is a directed graph with a node for each reachable state and an arc for each possible state change. We describe how symmetries of the modelled system can be exploited to obtain much more succinct state space analysis. The symmetries induce equivalence classes of states and equivalence classes of state changes. It is then possible to construct a condensed state space where each node represents an equivalence class of states while each arc represents an equivalence class of state changes. Such a condensed state space is often much smaller than the full state space and it is also much faster to construct. Nevertheless, it is possible to use the condensed state space to verify the same kind of behavioural properties as the full state space. hence, we do not lose analytic power. We define state spaces and condensed state spaces for a language called Coloured Petri Nets (CP-nets). This language is in widespread use for the modelling and analysis of concurrent systems. However, our techniques are general and they can be used for many other kinds of labelled transition systems. The paper does not assume that the reader is familiar with CP-nets (or Petri nets in general)—although such knowledge will, of course, be a help. The first four sections of the paper introduce the basic concepts of CP-nets. The next three sections deal with state spaces, condensed state spaces and computer tools for state space analysis. Finally, there is a short conclusion.