Petri nets are a model for the analysis of concurrent systems.

This book is a comprehensive, systematic survey of the synthesis problem, and of region theory which underlies its solution, covering the related theory, algorithms, and applications. The authors focus on safe Petri nets and place/transition nets (P/T-nets), treating synthesis as an automated process which, given behavioural specifications or partial specifications of a system to be realized, decides whether the specifications are feasible, and then produces a Petri net realizing them exactly, or if this is not possible produces a Petri net realizing an optimal approximation of the specifications. In Part I the authors introduce elementary net synthesis. In Part II they explain variations of elementary net synthesis and the unified theory of net synthesis. The first three chapters of Part III address the linear algebraic structure of regions, synthesis of P/T-nets from finite initialized transition systems, and the synthesis of unbounded P/T-nets. Finally, the last chapter in Part III and the chapters in Part IV cover more advanced topics and applications: P/T-net with the step firing rule, extracting concurrency from transition systems, process discovery, supervisory control, and the design of speed-independent circuits. Most chapters conclude with exercises, and the book is a valuable reference for both graduate students of computer science and electrical engineering and researchers and engineers in this domain.

With their intuitive graphical approach and expressive analysis techniques, Petri nets are suitable for a wide range of applications and teaching scenarios, and they have gained wide acceptance as a modeling technique in areas such as software design and control engineering. The core theoretical principles have been studied for many decades and there is now a comprehensive research literature that complements the extensive implementation experience. In this book the author presents a clear, thorough introduction to the essentials of Petri nets. He explains the core modeling techniques and analysis methods and he illustrates their usefulness with examples and case studies. Part I describes how to use Petri nets for modeling; all concepts are explained with the help of examples, starting with a generic, powerful model which is also intuitive and realistic. Part II covers the essential analysis methods that are specific to Petri nets, introducing techniques used to formulate key properties of system nets and algorithms for proving their validity. Part III presents case studies, each introducing new concepts, properties and analysis techniques required for very different modeling tasks. The author offers different paths among the chapters and sections: the elementary strand for readers who wish to study only elementary nets; the modeling strand for those who wish to study the modeling but not the analysis of systems; and finally the elementary models of the modeling strand for those interested in technically simple, but challenging examples and case studies. The author achieves an excellent balance between consistency, comprehensibility and correctness in a book of distinctive design. Among its characteristics, formal arguments are reduced to a minimum in the main text with many of the theoretical formalisms moved to an appendix, the explanations are supported throughout with fully integrated graphical illustrations, and each chapter ends with exercises and recommendations for further reading. The book is suitable for students of computer science and related subjects such as engineering, and for a broad range of researchers and practitioners.

Using formal methods for the specification and verification of hardware and software systems is becoming increasingly important as systems increase in size and complexity. The aim of the book is to illustrate progress in formal methods based on Petri net formalisms. It presents both practical and theoretical foundations for the use of Petri nets in complex system engineering tasks. In doing so it bridges the gap between Petri nets and the systems modeling and implementation process. It contains a collection of examples arising from different fields, such as flexible manufacturing, telecommunication and workflow management systems.

Net theory is a theory of systems organization which had its origins, about 20 years ago, in the dissertation of C. A. Petri [1]. Since this seminal paper, nets have been applied in various areas, at the same time being modified and theoretically investigated. In recent time, computer scientists are taking a broader interest in net theory. The main concern of this book is the presentation of those parts of net theory which can serve as a basis for practical application. It introduces the basic net theoretical concepts and ways of thinking, motivates them by means of examples and derives relations between them. Some extended examples il lustrate the method of application of nets. A major emphasis is devoted to those aspect which distinguish nets from other system models. These are for instance, the role of concurrency, an awareness of the finiteness of resources, and the pos sibility of using the same representation technique of different levels of ab straction. On completing this book the reader should have achieved a system atic grounding in the subject allowing him access to the net literature [25]. These objectives determined the subjects treated here. The presentation of the material here is rather more axiomatic than in ductive. We start with the basic notions of 'condition' and 'event' and the con cept of the change of states by (concurrently) occurring events. By generali zation of these notions a part of the theory of nets is presented.

Control of Discrete-event Systems provides a survey of the most important topics in the discrete-event systems theory with particular focus on finite-state automata, Petri nets and max-plus algebra. Coverage ranges from introductory material on the basic notions and definitions of discrete-event systems to more recent results. Special attention is given to results on supervisory control, state estimation and fault diagnosis of both centralized and distributed/decentralized systems developed in the framework of the Distributed Supervisory Control of Large Plants (DISC) project. Later parts of the text are devoted to the study of congested systems though fluidization, an over approximation allowing a much more efficient study of observation and control problems of timed Petri nets. Finally, the max-plus algebraic approach to the analysis and control of choice-free systems is also considered. Control of Discrete-event Systems provides an introduction to discrete-event systems for readers that are not familiar with this class of systems, but also provides an introduction to research problems and open issues of current interest to readers already familiar with them. Most of the material in this book has been presented during a Ph.D. school held in Cagliari, Italy, in June 2011.

Driven by the request for increased productivity, flexibility, and competitiveness, modern civilization increasingly has created high-performance discrete event dynamic systems (DEDSs). These systems exhibit concurrent, sequential, competitive activities among their components. They are often complex and large in scale, and necessarily flexible and thus highly capital-intensive. Examples of systems are manufacturing systems, communication networks, traffic and logistic systems, and military command and control systems. Modeling and performance evaluation play a vital role in the design and operation of such high-performance DEDSs and thus have received widespread attention from researchers over the past two decades. One methodology resulting from this effort is based on timed Petri nets and related graphical and mathematical tools. The popularity that Petri nets have been gaining in modeling of DEDSs is due to their powerful representational ability of concurrency and synchronization; however these properties of DEDSs cannot be expressed easily in traditional formalisms developed for analysis of `classical' systems with sequential behaviors. This book introduces the theories and applications of timed Petri nets systematically. Moreover, it also presents many practical applications in addition to theoretical developments, together with the latest research results and industrial applications of timed Petri nets. Timed Petri Nets: Theory and Application is intended for use by researchers and practitioners in the area of Discrete Event Dynamic Systems.