Petri nets: Properties, analysis and applications
01 Apr 1989-Vol. 77, Iss: 4, pp 541-580
TL;DR: The author proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis, and one section is devoted to marked graphs, the concurrent system model most amenable to analysis.
Abstract: Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets. >
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Book•
29 Oct 2010TL;DR: Industrial designers with a background in conventional (clocked) design to be able to understand asynchronous design sufficiently to assess what it has to offer and whether it might be advantageous in their next design task.
Abstract: Principles of Asynchronous Circuit Design - A Systems Perspective addresses the need for an introductory text on asynchronous circuit design. Part I is an 8-chapter tutorial which addresses the most important issues for the beginner, including how to think about asynchronous systems. Part II is a 4-chapter introduction to Balsa, a freely-available synthesis system for asynchronous circuits which will enable the reader to get hands-on experience of designing high-level asynchronous systems. Part III offers a number of examples of state-of-the-art asynchronous systems to illustrate what can be built using asynchronous techniques. The examples range from a complete commercial smart card chip to complex microprocessors. The objective in writing this book has been to enable industrial designers with a background in conventional (clocked) design to be able to understand asynchronous design sufficiently to assess what it has to offer and whether it might be advantageous in their next design task.
800 citations
Cites background from "Petri nets: Properties, analysis an..."
...1 Petri nets and STGs Briefly, a Petri net [3, 113, 94] is a graph composed of directed arcs and two types of nodes: transitions and places....
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Proceedings Article•
01 Jan 2003TL;DR: A Petri net-based algebra is proposed, used to model control flows, as a necessary constituent of reliable Web service composition process and is expressive enough to capture the semantics of complex Web service combinations.
Abstract: The Internet is going through several major changes. It has become a vehicle of Web services rather than just a repository of information. Many organizations are putting their core business competencies on the Internet as a collection of Web services. An important challenge is to integrate them to create new value-added Web services in ways that could never be foreseen forming what is known as Business-to-Business (B2B) services. Therefore, there is a need for modeling techniques and tools for reliable Web service composition. In this paper, we propose a Petri net-based algebra, used to model control flows, as a necessary constituent of reliable Web service composition process. This algebra is expressive enough to capture the semantics of complex Web service combinations.
705 citations
Cites background from "Petri nets: Properties, analysis an..."
...The verification of the correctness property consists in checking whether the underlying Petri net is live and bounded (Murata 1989)....
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...For more elaborate introduction to Petri nets, the reader is referred to (Murata 1989, Reisig 1985, Peterson 1981)....
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TL;DR: This paper reviews the recent development of relevant technologies from the perspectives of computer vision and pattern recognition, and discusses how to face emerging challenges of intelligent multi-camera video surveillance.
695 citations
Cites background from "Petri nets: Properties, analysis an..."
...There are also other features such as correlograms (Huang et al., 1997) and correlations (Savarese et al., 2006) to capture the co-occurrence of visual words over spatial kernels....
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TL;DR: In this paper, the authors present an approach to give formal semantics to Event-driven Process Chains (EPCs) by mapping EPCs (without connectors of type ∨) onto Petri nets.
Abstract: For many companies, business processes have become the focal point of attention. As a result, many tools have been developed for business process engineering and the actual deployment of business processes. Typical examples of these tools are Business Process Reengineering (BPR) tools, Enterprise Resource Planning (ERP) systems, and Workflow Management (WFM) systems. Some of the leading products, e.g. SAP R/3 (ERP/WFM) and ARIS (BPR), use Event-driven Process Chains (EPCs) to model business processes. Although the EPCs have become a widespread process modeling technique, they suffer from a serious drawback: neither the syntax nor the semantics of an EPC are well defined. In this paper, this problem is tackled by mapping EPCs (without connectors of type ∨) onto Petri nets. The Petri nets have formal semantics and provide an abundance of analysis techniques. As a result, the approach presented in this paper gives formal semantics to EPCs. Moreover, many analysis techniques are available for EPCs. To illustrate the approach, it is shown that the correctness of an EPC can be checked in polynomial time by using Petri-net-based analysis techniques.
693 citations
References
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01 Jan 1962
TL;DR: The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem and a theory of communication is proposed that yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata.
Abstract: Diese Arbeit befasst sich mit den begrifflichen Grundlagen einer Theorie der Kommunikation. Die Aufgabe dieser Theorie soll es sein, moglichst viele Erscheinungen bei der Informationsubertragung und Informationswandlung in einheitlicher und exakter Weise zu beschreiben.
The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem. The argument proceeds as follows:
1. We assume the following postulates:
a) there exists an upper bound on the speed of signals;
b) there exists an upper bound on the density with which information can be stored.
2. Automata of fixed, finite size can recognize, at best, only iteratively defined classes of input sequences. (See Kleene (11) and Copi, Elgot, and Wright (8).)
3. Recursively defined classes of input sequences that cannot be defined iteratively can be recognized only by automata of unbounded size.
4. In order for an automaton to solve a (soluble) recursive problem, the possibility must be granted that it can be extended unboundedly in whatever way might be required.
5. Automata (as actual hardware) formulated in accordance with automata theory will, after a finite number of extensions, conflict with at least one of the postulates named above.
Suitable conceptual structures for an exact theory of communication are then discussed, and a theory of communication proposed.
All of the really useful results of automata theory may be expressed by means of these new concepts. Moreover, the results retain their usefulness and the new nrocedure has definite advantages over the older ones.
The proposed representation differs from each of the presently known theories concerning information on at least one of the following essential points:
1. The existence of a metric is assumed for either space nor time nor for other physical magnitudes.
2. Time is introduced as a strictly local relation between states.
3. The objects of the theory are discrete, and they are combined and produced only by means of strictly finite techniques.
The following conclusions drawn from the results of this work may be cited as of some practical interest:
1. The tolerance requirements for the response characteristics of computer components can be substantially weakened if the computer is suitably structured.
2. It is possible to design computers structurally in such a way that they are asynchronous, all parts operating in parallel, and can be extended arbitrarily without interrupting their computation.
3. For complicated organizational processes of any given sort the theory yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata.
2,523 citations
TL;DR: It is shown that GSPN are equivalent to continuous-time stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented.
Abstract: Generalized stochastic Petri nets (GSPNs) are presented and are applied to the performance evaluation of multiprocessor systems. GSPNs are derived from standard Petri nets by partitioning the set of transitions into two subsets comprising timed and immediate transitions. An exponentially distributed random firing time is associated with each timed transition, whereas immediate transitions fire in zero time. It is shown that GSPN are equivalent to continuous-time stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented. Examples of application of gspn models to the performance evaluation of multiprocessor systems show the usefulness and the effectiveness of this modeling tool. 15 references.
1,394 citations
TL;DR: An isomorphism between the behavior of Petri nets with exponentially distributed transition rates and Markov processes is presented and this work solves for the steady state average message delay and throughput on a communication link when the alternating bit protocol is used for error recovery.
Abstract: An isomorphism between the behavior of Petri nets with exponentially distributed transition rates and Markov processes is presented. In particular, k-bounded Petri nets are isomorphic to finite Markov processes and can be solved by standard techniques if k is not too large. As a practical example, we solve for the steady state average message delay and throughput on a communication link when the alternating bit protocol is used for error recovery.
1,090 citations
TL;DR: This paper introduces a model called the parallel program schema for the representation and study of programs containing parallel sequencing, related to Ianov's program schema, but extends it, both by modelling memory structure in more detail and by admitting parallel computation.
1,040 citations
TL;DR: The time-Petri net (TPN) appears to be a suitable model for the study of practical recoverable processes and several practical communication protocols are formally designed and analyzed using this new model.
Abstract: A study is presented which permits the formal analysis and synthesis of recoverable computer communication protocols. This study is based on a formal representation of processes by a model of computation, the Petri nets (PN's). The PN model is generalized to include a representation of the possible failures, and then, the concept of "recoverability" is formally defined. A set of necessary and sufficient conditions which a process must satisfy in order to be recoverable is derived. In the PN model, the processes that satisfy these conditions are shown to have some practical limitations. A new model, the time-Petri net (TPN), is introduced to remove these limitations. This new model allows the introduction of constraints in the execution times of its part. As shown in this paper, the TPN appears to be a suitable model for the study of practical recoverable processes. Several practical communication protocols are formally designed and analyzed using this new model, and some interesting properties of these protocols are formally derived.
917 citations