Showing papers on "Petri net published in 1994"

Synchronization and Linearity: An Algebra for Discrete Event Systems

Abstract: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the 'max-plus algebra'. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide 'discrete event system theory', which is shown to parallel the classical linear system theory in several ways.

Petri nets and industrial applications: A tutorial

Abstract: Petri nets, as a graphical and mathematical tool, provide a uniform environment for modelling, formal analysis, and design of discrete event systems. The main objective of this paper is to introduce the fundamental concepts of Petri nets to researchers and practitioners, both from academia and industry, who are involved in the work in the areas of modelling and analysis of industrial types of systems, as well as those who may potentially be involved in these areas. The paper begins with an overview of applications of Petri nets, mostly industrial ones. Then, it proceeds with a description of Petri nets, properties, and analysis methods. The discussion of properties is put in the context of industrial applications. The analysis methods are illustrated using an example of a simple robotic assembly system. The performance analysis, using Petri nets, is discussed for deterministic and stochastic Petri nets. The presented techniques are illustrated by examples representing simple production systems. In addition, the paper introduces high-level Petri nets, fuzzy Petri nets, and temporal Petri nets. This is done in the context of application prospects. The paper also briefly discusses some of the reasons restricting the use of Petri nets, mostly, to academic institutions. >

Feedback control of Petri nets based on place invariants

Abstract: This paper describes a method for constructing a Petri net feedback controller for a discrete event system modeled by a Petri net. The controller enforces a set of linear constraints on the plant and consists of places and arcs. It is computed using the concept of Petri net place invariants. The size of the controller is proportional to the number of constraints which must be satisfied. The method is very attractive computationally, and it makes possible the systematic design of Petri net controllers for complex industrial systems. >

Scheduling flexible manufacturing systems using Petri nets and heuristic search

Abstract: Petri net modeling combined with heuristic search provides a new scheduling method for flexible manufacturing systems. The method formulates a scheduling problem with a Petri net model. Then, it generates and searches a partial reachability graph to find an optimal or near optimal feasible schedule in terms of the firing sequence of the transitions of the Petri net model. The method can handle features such as routing flexibility, shared resources, lot sizes and concurrency. By following the generated schedule, potential deadlocks in the Petri net model and the system can be avoided. Hence the analytical overhead to guarantee the liveness of the model and the system is eliminated. Some heuristic functions for efficient search are explored and the experimental results are presented. >

Detecting composite events in active database systems using Petri nets

Abstract: The detection of events in an active database system turns out to be a difficult problem due to the expressive event specification languages proposed in the recent past which include, among others, complexly defined events (composite events). Therefore, a mechanism is required that is suitable to model the semantics of composite events and to implement the event detector. We demonstrate how Petri nets can be used as the basis of such a mechanism in the context of the SAMOS active database system prototype. >

Dispatching-driven deadlock avoidance controller synthesis for flexible manufacturing systems

Abstract: This paper develops a new method for synthesizing deadlock avoidance controllers (DACs) that realize job and machine dispatching policies of a flexible manufacturing system (FMS) into deadlock free control actions. Such controllers not only keep the FMS capable of repeating any of its operations, but also achieve a high resource utilization under any given dispatching policy. Our methodology is based on an untimed Petri net formalism. It consists of four ingredients: 1) a bottom-up approach for synthesizing a controlled production Petri net (CPPN) model of a FMS; 2) a necessary and sufficient liveness condition based on decomposition of the CPPN into controlled production subnets and the concept of minimal resource requirements; 3) a sufficient procedure to test whether the liveness condition is kept after a control action is executed; and 4) an algorithm that combines the test procedure with the given dispatching policy to generate valid and utilization maximizing control actions. We assess that this method is of polynomial time complexity and show that it results in a much larger class of controls than that of an existing deadlock avoidance scheme. >

A characterization of the stochastic process underlying a stochastic Petri net

Abstract: Stochastic Petri nets (SPN's) with generally distributed firing times can model a large class of systems, but simulation is the only feasible approach for their solution. We explore a hierarchy of SPN classes where modeling power is reduced in exchange for an increasingly efficient solution. Generalized stochastic Petri nets (GSPN's), deterministic and stochastic Petri nets (DSPN's), semi-Markovian stochastic Petri nets (SM-SPN's), timed Petri nets (TPN's), and generalized timed Petri nets (GTPN's) are particular entries in our hierarchy. Additional classes of SPN's for which we show how to compute an analytical solution are obtained by the method of the embedded Markov chain (DSPN's are just one example in this class) and state discretization, which we apply not only to the continuous-time case (PH-type distributions), but also to the discrete case. >

Models for Concurrency

Abstract: This report surveys a range of models for parallel computation to include interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like Petri nets, asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces where concurrency is represented more explicitly by a form of causal independence. The presentation is unified by casting the models in a category-theoretic framework. One aim is to use category theory to provide abstract characterisations of constructions like parallel composition valid throughout a range of different models and to provide formal means for translating between different models. A knowledge of basic category theory is assumed, up to an acquaintance with the notion of adjunction.

A generalized fuzzy Petri net model

Abstract: 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. >

Petri Net Analysis Using Boolean Manipulation

Abstract: This paper presents a novel analysis approach for bounded Petri nets. The net behavior is modeled by boolean functions, thus reducing reasoning about Petri nets to boolean calculation. The state explosion problem is managed by using Binary Decision Diagrams (BDDs), which are capable to represent large sets of markings in small data structures. The ability of Petri nets to model systems, the flexibility and generality of boolean algebras, and the efficient implementation of BDDs, provide a general environment to handle a large variety of problems. Examples are presented that show how all the reachable states (1018) of a Petri net can be efficiently calculated and represented with a small BDD (103 nodes). Properties requiring an exhaustive analysis of the state space can be verified in polynomial time in the size of the BDD.

Power-hierarchy of dependability-model types

Abstract: This paper formally establishes a hierarchy, among the most commonly used types of dependability models, according to their modeling power. Among the combinatorial (non-state-space) model types, we show that fault trees with repeated events are the most powerful in terms of kinds of dependencies among various system components that can be modeled. Reliability graphs are less powerful than fault trees with repeated events but more powerful than reliability block diagrams and fault trees without repeated events. By virtue of the constructive nature of our proofs, we provide algorithms for converting from one model type to another. Among the Markov (state-space) model types, we consider continuous-time Markov chains, generalized stochastic Petri nets, Markov reward models, and stochastic reward nets. These are more powerful than combinatorial-model types in that they can capture dependencies such as a shared repair facility between system components. However, they are analytically tractable only under certain distributional assumptions such as exponential failure- and repair-time distributions. They are also subject to an exponentially large state space. The equivalence among various Markov-model types is briefly discussed. >

Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution

Abstract: In a previous paper we have defined Superposed Stochastic Automata (SSA) [13], a class of Stochastic Petri Nets (SPN) whose solution can be efficiently computed since it never requires the construction of the complete Markov chain of the underlying Markovian process. The efficient solution of SSA is based on a method proposed by Plateau in [23] for the analysis of stochastic processes generated by the composition of stochastic automata. Efficient analysis is there achieved (both in terms of space and time) with a technique based on Kronecker (tensor) algebra for matrices.

Fuzzy reasoning supported by Petri nets

Abstract: We develop a representational model for the knowledge base (KB) of fuzzy production systems with rule chaining based on the Petri net formalism. The model presents the execution of a KB following a data driven strategy based on the sup-min compositional rule of inference. In this connection, algorithms characterizing different situations have been described, including the case where the KB is characterized by complete information about all the input variables and the case where it is characterized by ignorance of some of these variables. For this last situation we develop a process of "incremental reasoning"; this process allows the KB to take information about previously unknown values into consideration as soon as such information becomes available. Furthermore, as compared to other solutions, the rule chaining mechanism we introduce is more flexible, and the description of the rules more generic. The computational complexity of these algorithms is O((C/2+M+N)R/sup 2/) for the "complete information" case and O((M+N)R/sup 2/) and O(2(M+N)R/sup 2/) for the other cases, where R is the number of fuzzy conditional statements of the KB, M and N the maximum number of antecedents and consequents in the rules and C the number of chaining transitions in the KB representation. >

An Introduction to the Theoretical Aspects of Coloured Petri Nets

Abstract: This paper presents the basic theoretical aspects of Coloured Petri Nets (CP-nets or CPN). CP-nets have been developed, from being a promising theoretical model, to being a full-fledged language for the design, specification, simulation, validation and implementation of large software systems (and other systems in which human beings and/or computers communicate by means of some more or less formal rules). The paper contains the formal definition of CP-nets and their basic concepts (e.g., the different dynamic properties such as liveness and fairness). The paper also contains a short introduction to the analysis methods, in particular occurrence graphs and place invariants. The development of CP-nets 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 that we find 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 the description of the synchronisation of concurrent processes, while programming languages provide the primitives for the definition of data types and the manipulation of their data values.

Generating basis siphons and traps of Petri nets using the sign incidence matrix

Abstract: This paper introduces a new matrix called the sign incidence matrix for Petri nets. Using this sign incidence matrix, we present a simple algorithm for generating all basis siphons or traps without first generating all siphons or traps. Any siphon (trap) can be expressed as an union of basis siphons (basis traps). The concept of siphons and traps plays an important role in the analysis of Petri nets. In particular, criteria for liveness and reachability of some subclasses of Petri nets can be stated in terms of siphons and traps. >

Information Systems Engineering: A Formal Approach

Abstract: Engineers and scientists need powerful formalisms to make conceptual models of systems in order to analyze and design them. These models can be used to verify the behavior of the systems, or as an executable specification of them. In this book, Professor van Hee concentrates on discrete dynamic systems, e.g. computer hardware, and information and logistical systems. He develops an integrated formalism that can be used as a prototyping language. It has three components: Petri nets, extended with time, token values and hierarchy; a specification language that is a subset of Z; and a binary data model, extended with complex objects. Much attention is paid to methods for constructing models of systems and analyzing their behavior, i.e., putting the theory into practice. The book is aimed at graduate students and researchers in computer science, electrical engineering, and applied mathematics.

Comparing ladder logic diagrams and Petri nets for sequence controller design through a discrete manufacturing system

Abstract: Design methods for sequence controllers play a very important role in advancing industrial automation. The increasing complexity and varying needs of modern discrete manufacturing systems have challenged the traditional design methods such as the use of ladder logic diagrams (LLDs) for programmable logic controllers. The methodologies based on research results in computer science have recently received growing attention by academic researchers and industrial engineers in order to design flexible, reusable, and maintainable control software. Particularly, Petri nets are emerging as a very important tool to provide an integrated solution for modeling, analysis, simulation, and control of industrial automated systems. This paper identifies certain criteria to compare LLDs and Petri nets in designing sequence controllers and responding to the changing control requirements. The comparison is performed through a practical system after introducing "real-time Petri nets" for discrete-event control purposes. The results reported in this paper will help: (a) further establish Petri net based techniques for discrete-event control of industrial automated systems; and (b) effectively convince industrial practitioners and researchers that it is worthy and timely to consider and promote the applications of Petri nets to their particular discrete-event control problems. >

Coloured Petri Nets Extended with Channels for Synchronous Communication

Abstract: This paper shows how Coloured Petri Nets (CP-nets) can be extended to support synchronous communication. We introduce coloured communication channels through which transitions are allowed to communicate complex values. Small examples show how channel communication is convenient for creating compact and comprehensive models.

Decidability Issues for Petri Nets

Abstract: This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties , various behavioural equivalences and finally the model checking problem for temporal logics .

Proving properties of real-time systems through logical specifications and Petri net models

Abstract: Addresses the problem of formally analyzing the properties of real-time systems. We propose a method based on modeling the system as a timed Petri net and on specifying its properties in TRIO, an extension of temporal logic suitable for dealing explicitly with time and for measuring it. Timed Petri nets are axiomatized in terms of TRIO, so that their properties can be derived as theorems in the same spirit as the classical Hoare method allows one to prove properties of programs coded in a Pascal-like language. The method is also illustrated through an example. >

Automated transformation of algorithms into register-transfer level implementations

Abstract: This paper describes a high-level synthesis system, called CAMAD, for transforming algorithms into hardware implementation structures at register-transfer level. The algorithms are used to specify the behaviors of the hardware to be designed. They are first translated into a formal representation model which is based on timed Petri nets and consists of separate but related descriptions of control and data path. The formal model is used as an intermediate design representation and supports an iterative transformation approach to high-level synthesis. The basic idea is that once the behavioral specification is translated into the initial design representation, it can be viewed as a primitive implementation. Correctness-preserving transformations are then used to successively transform the initial design into an efficient implementation. Selection of transformations is guided by an optimization strategy which makes design decisions concerning operation scheduling, data path allocation, and control allocation simultaneously. The integration of these several synthesis subtasks has resulted in a better chance to reach the globally optimal solution. Experimental results show that our approach produces improved register-transfer designs, especially in the cases when the designed hardware consists of data paths and control logics that are tightly coupled. >

On the power of bounded concurrency I: finite automata

Abstract: We investigate the descriptive succinctness of three fundamental notions for modeling concurrency: nondeterminism and pure parallelism, the two facets of alternation, and bounded cooperative concurrency, whereby a system configuration consists of a bounded number of cooperating states. Our results are couched in the general framework of finite-state automata, but hold for appropriate versions of most concurrent models of computation, such as Petri nets, statecharts or finite-state versions of concurrent programming languages. We exhibit exhaustive sets of upper and lower bounds on the relative succinctness of these features over Σ* and Σω, establishing that:(1) Each of the three features represents an exponential saving in succinctness of the representation, in a manner that is independent of the other two and additive with respect to them.(2) Of the three, bounded concurrency is the strongest, representing a similar exponential saving even when substituted for each of the others.For example, we prove exponential upper and lower bounds on the simulation of deterministic concurrent automata by AFAs, and triple-exponential bounds on the simulation of alternating concurrent automata by DFAs.