Wolfgang Reisig

The non-sequential behaviour of Petri nets

The idea of representing non-sequential processes as partially ordered sets (occurrence nets) is applied to place/transition nets (Petri nets), based on the well known notion of process for condition/event-systems. For occurrence nets some theorems relating K -density, cut finiteness, and discreteness are proved. With these theorems the result that a place/transition net is bounded if and only if its processes are K -dense is obtained.

Petri nets and algebraic specifications

Reisig, W., Petri nets and algebraic specifications, Theoretical Computer Science 80 (1991) 1-34. Petri nets gain a great deal of modelling power by representing dynamically changing items as structured tokens (instead of “black dots”). Algebraic specifications turned out adequate for dealing with structured items. We will use this formalism to construct Petri nets with structured tokens. Place- and transition-invariants are useful analysis techniques for conventional Petri nets. We derive corresponding formalisms for nets with structured tokens, based on term substitution.

Lectures on Concurrency and Petri Nets

Over the last decade there has been a shift from “data-aware” information systems to “process-aware” information systems. To support business processes an enterprise information system needs to be aware of these processes and their organizational context. Business Process Management (BPM) includes methods, techniques, and tools to support the design, enactment, management, and analysis of such operational business processes. BPM can be considered as an extension of classical Workflow Management (WFM) systems and approaches. This tutorial introduces models, systems, and standards for the design, analysis, and enactment of workflow processes. Petri nets are used for the modeling and analysis of workflows. Using Petri nets as a formal basis, contemporary systems, languages, and standards for BPM and WFM are discussed. Although it is clear that Petri nets can serve as a solid foundation for BPM/WFM technology, in reality systems, languages, and standards are developed in an ad-hoc fashion. To illustrate this XPDL, the “Lingua Franca” proposed by the Workflow Management Coalition (WfMC), is analyzed using a set of 20 basic workflow patterns. This analysis exposes some of the typical semantic problems restricting the application of BPM/WFM technology.

Place or Transition Petri Nets

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.

An Operating Guideline Approach to the SOA

Interorganizational cooperation is more and more organized by the paradigm of services. The service-oriented architecture (SOA) provides a general framework for service interaction. It describes three roles, service provider, service requester, and service broker, together with the three operations publish, find, and bind. We provide a formal method based on Petri nets to model services and their cooperation. We characterize well-behaving pairs of requester’s and provider’s services and suggest operating guidelines as a convenient and intuitive artifact to realize publish. Then, the find operation reduces to a matching problem between the requester’s service and the operating guideline. Binding of a requester’s and a provider’s service is therefore guaranteed to result in a well-behaving cooperating service.

Petri Nets: Applications and Relationships to Other Models of Concurrency

We may not be able to make you love reading, but petri nets central models and their properties advances in petri nets 1986 part 1 proceedings of an advanced course bad honnef 8 19 september 1 will lead you to love reading starting from now. Book is the window to open the new world. The world that you want is in the better stage and level. World will always guide you to even the prestige stage of the life. You know, this is some of how reading will give you the kindness. In this case, more books you read more knowledge you know, but it can mean also the bore is full.

The synthesis problem of Petri nets

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.

Inter-operability of Workflow Applications: Local Criteria for Global Soundness

Automatic analysis techniques for business processes are crucial for todays workflow applications. Since business processes are rapidly changing, only fully automatic techniques can detect processes which might cause deadlocks or congestion. Analyzing a complete workflow application, however, is much too complex to be performed fully automatically. Therefore, techniques for analyzing single processes in isolation and corresponding soundness criteria have been proposed. Though these techniques may detect errors such as deadlocks or congestion, problems arising from an incorrect inter-operation with other processes are completely ignored. The situation becomes even worse for cross-organizational workflow applications, where some processes are not even available for analysis due to confidentiality reasons. We propose a technique which allows to detect but a few errors of workflow applications which arise from incorrect inter-operation of workflows. To this end, the dynamics of the inter-operation of different workflows must be specified by the help of sequence diagrams. Then, each single workflow can be checked for local soundness with respect to this specification. If each single workflow is locally sound, a composition theorem guarantees global soundness of the complete workflow application. This way, each organization can check its own workflows without knowing the workflows of other organizations--still global soundness is guaranteed.

Modeling in Systems Biology: The Petri Net Approach

The emerging, multi-disciplinary field of systems biology is devoted to the study of the relationships between various parts of a biological system, and computer modeling plays a vital role in the drive to understand the processes of life from an holistic viewpoint. Advancements in experimental technologies in biology and medicine have generated an enormous amount of biological data on the dependencies and interactions of many different molecular cell processes, fueling the development of numerous computational methods for exploring this data. The mathematical formalism of Petri net theory is able to encompass many of these techniques. This essential text/reference presents a comprehensive overview of cutting-edge research in applications of Petri nets in systems biology, with contributions from an international selection of experts. Those unfamiliar with the field are also provided with a general introduction to systems biology, the foundations of biochemistry, and the basics of Petri net theory. Further chapters address Petri net modeling techniques for building and analyzing biological models, as well as network prediction approaches, before reviewing the applications to networks of different biological classification. Topics and features: investigates the modular, qualitative modeling of regulatory networks using Petri nets, and examines an Hybrid Functional Petri net simulation case study; contains a glossary of the concepts and notation used in the book, in addition to exercises at the end of each chapter; covers the topological analysis of metabolic and regulatory networks, the analysis of models of signaling networks, and the prediction of network structure; provides a biological case study on the conversion of logical networks into Petri nets; discusses discrete modeling, stochastic modeling, fuzzy modeling, dynamic pathway modeling, genetic regulatory network modeling, and quantitative analysis techniques; includes a Foreword by Professor Jens Reich, Professor of Bioinformatics at Humboldt University and Max Delbrck Center for Molecular Medicine in Berlin. This unique guide to the modeling of biochemical systems using Petri net concepts will be of real utility to researchers and students of computational biology, systems biology, bioinformatics, computer science, and biochemistry.

Petri nets in software engineering

Software engineering and Petri net theory are disciplines of different nature. Research on software engineering focuses on a problem domain, i.e., the development of complex software systems, and tries to find a coherent set of solutions to cope with the different aspects of the problem, while research on Petri nets investigates applications and properties of a specific model (Petri nets). When Petri nets can solve some problems of software development, the two disciplines meet with mutual benefits: software engineers may find useful solutions, while Petri net experts may find new stimuli and challenges in their domain. Petri nets and software engineering have similar age: Karl Adam Petri wrote his thesis in 1962, while the term software engineering was coined in 1968 at a NATO conference held in Germany. The two disciplines met several times in the past forty years with alternate fortune. Presently, software engineering and Petri nets do not find many meeting points, as witnessed by the scarce references to Petri nets in software engineering journals and conferences and vice versa, but software engineering is facing many new challenges and the Petri net body of knowledge is extending with new results. This paper attempts to illustrate the many dimensions of software engineering, to point at some aspects of Petri nets that have been or can be exploited to solve software engineering problems, and to identify new software engineering challenges that may be solved with Petri net results. This paper does not have the ambition of completely surveying either discipline, but hopes to help scientists and practitioners in identifying interesting areas where software engineers and Petri net experts can fruitfully collaborate 1 .The central issue of this contribution is a methodology for the use of nets in practical systems design. We show how nets of channels and agencies allow for a continuous and systematic transition from informal and unprecise to precise and formal specifications. This development methodology leads to the representation of dynamic systems behaviour (using Pr/T-Nets) which is apt to rapid prototyping and formal correctness proofs.