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.

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.

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 Delbruck 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 provide a formal framework for system modeling and validation which has proven to be very reliable in practice. This book presents variousnet models appropriate for designing specific systems, where systems are understood very generally as "organizational systems" in which regulatedflows of objects and information are significant. The models are interrelated in the sense that they have common interpretation patterns: together they can be understood as a method for specifying any given system or any section of such a system to any given degree of refinement. The simple and immediately understandable principles of system modelling with nets makes it possible to provide an illustrated description of this method without going into the mathematics behind it. The text is based on courses the author developed for project engineers and project managers in the area of embedded computer 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.

Distributed Computing is rapidly becoming the principal computing paradigm in diverse areas of computing, communication, and control. Processor clusters, local and wide area networks, and the information highway evolved a new kind of problems which can be solved with distributed algorithms. In this textbook a variety of distributed algorithms are presented independently of particular programming languages or hardware, using the graphically suggestive technique of Petri nets which is both easy to comprehend intuitively and formally rigorous. By means of temporal logic the author provides surprisingly simple yet powerful correctness proofs for the algorithms. The scope of the book ranges from distributed control and synchronization of two sites up to algorithms on any kind of networks. Numerous examples show that description and analysis of distributed algorithms in this framework are intuitive and technically transparent.

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 Delbruck 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."

The very ?rst model of concurrent and distributed systems was introduced by C.A. Petri in his seminal Ph.D. thesis in 1964. Petri nets has remained a central model for concurrentsystemsfor40 years,andthey areoften usedasa yardstick for other models of concurrency. As a matter of fact, many other models have been developed since then, and this research area is ?ourishing today. The goal of the 4th Advanced Course on Petri Nets held in Eichsta ..tt, Germany in September 2003 was to present applications and the theory of Petri Nets in the context of a whole range of other models. We believe that in this way the participants of the course received a broad and in-depth picture of research in concurrent and distributed systems. It is also the goal of this volume to convey this picture. The volume is based on lectures given at the Advanced Course, but in order to provide a balanced p- sentation of the ?eld, some of the lectures are not included, and some material not presented in Eichst. att is covered here. In particular, a series of introductory lectures was not included in this volume, as the material they covered is well - tablishedby now,andwellpresentedelsewhere (e.g.,inW. ReisigandG. Roz- berg, eds., "Lectures on Petri Nets," LNCS 1491, 1492, Springer-Verlag, 1997 - these two volumes are based on the 3rd Advanced Course on Petri Nets).

This volume contains the proceedings of the 25th International Conference on Application and Theory of Petri Nets (ICATPN 2004). The aim of the Petri net conferences is to create a forum for discussing progress in the application and theory of Petri nets. Typically, the conferenceshave 100-150participants, one third of these c- ing from industry, whereas the others are from universities and research insti- tions. The conferences always take place in the last week of June. The conference and a number of other activities are coordinated by a ste- ing committee with the following members: Wil van der Aalst (The Neth- lands), JonathanBillington(Australia), JrgDesel(Germany), SusannaDonatelli (Italy), SergeHaddad(France), KurtJensen(Denmark), MaciejKoutny(United Kingdom), Sadatoshi Kumagai(Japan), GiorgioDe Michelis (Italy), Tadao- rata (USA), Carl Adam Petri (Germany, Honorary Member), Wolfgang Reisig (Germany), GrzegorzRozenberg(TheNetherlands, Chairman)andManuelSilva (Spain). The 2004 conference was organized by the Department of Computer Science of the University of Bologna, Italy. We would like to thank the organizing c- mittee, chaired by Roberto Gorrieri, for the e?ort invested in making the event successful. We are also grateful to the following sponsoring institutions and - ganizations: Associazione Italiana per l'Informatica ed il Calcolo Automatico (AICA), Microsoft Research, and Network Project & Solutions (NPS Group). We received a total of 62 submissions from 26 di?erent countries. The p- gramcommittee?nallyselected19regularpapersand5toolpresentationpapers. This volume comprises the papers that were accepted for presentation. Invited lectures were given by Gianfranco Ciardo, Roberto Gorrieri, Thomas A. H- zinger, Wojciech Penczek, Lucia Pomello and William H. Sanders. Their papers are also included in this volume.

This volume, "Petri Net Technology for Communication-Based Systems," is a state-of-the-artreportin the seriesAdvances in Petri Nets. It showshowvarious well-established and new Petri net notions and techniques can be used for m- elingcommunication-basedsystems, withspecialfocusonwork?owmanagement and business processes. In the last 6 years this topic has been studied by the DFG Forschergruppe Petri Net Technology in Berlin in close cooperation with the international c- munity. The main results of this cooperation were presented at the 1st and 2nd InternationalColloquiaonPetriNetTechnologiesforModelingCommunication- Based Systems, held in Berlin in 1999 and 2001, respectively. A careful selection of contributions by members of the DFG Forschergruppe and by international experts in this ?eld are presented in this volume. Taking into account the fru- ful discussions during the two colloquia and the cross-refereeing process for the accepted papers, a high degree of common understanding was achieved, leading to a highly comprehensive presentation in this volume. The topics of the papers in this volume can be roughly classi?ed into the following two areas: - Petri net technology and - application to communication-based systems. Since most papers comprise aspects of both areas, we chose an alphabetic order. However, in the following we give a rough overview of the contributions in both areas according to the main focus of the corresponding papers.

The two-volume set originates from the Advanced Course on Petri Nets held in Dagstuhl, Germany in September 1996; beyond the lectures given there, additional chapters have been commissioned to give a well-balanced presentation of the state of the art in the area.
Together with its companion volume "Lectures on Petri Nets II: Applications" this book is the actual reference for the area and addresses professionals, students, lecturers, and researchers who are
- interested in systems design and would like to learn to use Petri nets familiar with subareas of the theory or its applications and wish to view the whole area
- interested in learning about recent results presented within a unified framework
- planning to apply Petri nets in practical situations
- interested in the relationship of Petri nets to other models of concurrent systems.

The two-volume set originates from the Advanced Course on Petri Nets held in Dagstuhl, Germany in September 1996; beyond the lectures given there, additional chapters have been commissioned to give a well-balanced presentation of the state of the art in the area.
Together with its companion volume "Lectures on Petri Nets I: Basic Models" this book is the actual reference for the area and addresses professionals, students, lecturers, and researchers who are
- interested in systems design and would like to learn to use Petri nets familiar with subareas of the theory or its applications and wish to view the whole area
- interested in learning about recent results presented within a unified framework
- planning to apply Petri nets in practical situations
- interested in the relationship of Petri nets to other models of concurrent systems.

Distributed Computing is rapidly becoming the principal computing paradigm in diverse areas of computing, communication, and control. Processor clusters, local and wide area networks, and the information highway evolved a new kind of problems which can be solved with distributed algorithms.In this textbook a variety of distributed algorithms are presented independently of particular programming languages or hardware, using the graphically suggestive technique of Petri nets which is both easy to comprehend intuitively and formally rigorous. By means of temporal logic the author provides surprisingly simple yet powerful correctness proofs for the algorithms.The scope of the book ranges from distributed control and synchronization of two sites up to algorithms on any kind of networks. Numerous examples show that description and analysis of distributed algorithms in this framework are intuitive and technically transparent.

This book constitutes the refereed proceedings of the 17th International Conference on Application and Theory of Petri Nets, held in Osaka, Japan, in June 1996.
The 26 revised full papers included in the book together with three invited presentations were selected from a total of 78 submissions. The book addresses the current theoretical and applicational aspects of the various types of Petri Nets and competently reflects the state of the art in the area.

Petri Nets represent a long and sustained effort. to develop concepts, theories and tools to aid in design and analysis of concurrent systems. They are used in many areas of computer science including software engineering, data base and in formation systems, computer architecture and operating systems, communication protocols and computer networks, process control, and socio-technical systems such as office communication and man-machine interaction. Quite substantial theory has been developed for Petri Nets. It reflects all major problem areas of concurrent distributed systems and covers many successfully applied principles and analysis techniques for systems organisation. Since the time that C. A. Petri has presented his original ideas, a rich body of knowledge has been developed-a recent bibliography (in Advances in Petri Nets 1981) includes more than 2000 entries. Already in 1979 an Advanced Course on Petri Nets was organized in Hamburg, West Germany, aiming at systematizing the existing knowledge and making it well accessible to a wide audience of computer scientists interested in theory and applications of concurrent systems. This course has turned out to be successful in the sense that it has initiated a lot of new research into applications and theory of Petri Nets. This had led to. another Advanced Course in 1986 in Bad Honnef, West Germany - where during two weeks more than 30 lectures were presented covering the most important current developments in the area of Petri Nets."

The present volume is the second of two parts which constitute the proceedings of the 1986 Advanced Course on Petri Nets in Bad Honnef. It discusses tools supporting the design of petri nets as well as their modification and analysis, presents a variety of applications, and covers the relationship of petri nets to other concurrency models. These current issues of the "Advances in Petri Nets" present the most significant recent results in the application and theory of petri nets to the broad computer science community. They particularly address those who are: - interested in systems design and would like to learn to use petri nets, - familiar with subareas of the theory or the applications of nets and wish to become acquainted with the whole area, - interested in learning about recent results presented within a unified framework, - going to learn about successfully applying petri nets in - various practical situations, - interested in the relationship of petri nets to other models of concurrent systems.

This volume documents the progress of application and theory of Petri Nets since the Advanced Course on General Net Theory of Processes and Systems, held in Hamburg, October 8-19, 1979, This course presen ted in detail wha t had been achieved in this area since the first studies of concurrent systems 20 years ago, After this course it seemed worthwhile to establish a co-operation between different groups working in the field of Petri N ets, The starting points were the AFCET Special Interest Group "Systemes Paralleles et Distribues" and the Gl Special Interest Group "Petrinetze und verwandte Systemmodelle", Meanwhile, group s of many European countries are involved, A main activity of this co-operation is the realization of workshops in varying European countries, The first workshop of this kind was carried out in Strasbourg (France), September 23-26, 1980, The second one took place in Bad Honnef (Germany) September 28-30, 1981. This volume contains contributions of these two workshops, The 1980 workshop in Strasbourg was partitioned into 6 topics : (1) Application of Nets to Realtime Systems, (2) Programming Languages and Software Engineering, (3) Information Flow and Concurrency, (4) Net Morphisms and High Level Petri Nets, (5) Mathematical Analysis and N et Languages, (6) Reliability and Recovery Issues, In this volume, the chairman of each topic gives a short introduction to his area whict should help to understand its specific problems and to in troduce the presented papers,

This book offers an overview of the key ideas of Petri nets, how they were developed, and how they were applied in diverse applications. The chapters in the first part offer individual perspectives on the impact of Petri's work. The second part of the book contains personal memories from researchers who collaborated with him closely, in particular they recount his unique personality. The chapters in the third part offer more conventional treatments on various aspects of current Petri net research, and the fourth part examines the wide applications of Petri nets, and the relationships with other domains. The editors and authors are the leading researchers in this domain, and this book will be a valuable insight for researchers in computer science, particularly those engaged with concurrency and distributed systems.

"Systementwurf mit Netzen" lautet der Titel dieses Buches. Was ist darun- ter zu verstehen? Genauer: was ist bier mit Systemen, was mit Netzen gemeint? Beginnen wir mit den Systemen: sie sind in diesem Buch sehr aIlgemein aufgefaBt als "organisatorische Systeme", in denen geregelte Flusse von Gegenstanden und Informationen bedeutsam sind. Unter den Netzen wie- derum wollen wir bier solche verstehen, wie sie im Rahmen der Netztheorie nach C. A. Petri entwickelt wurden: sogenannte "Petrinetze". Diese Petri- netze haben sich in der Praxis entschieden bewahrt. Wir werden im Verlauf des Buches verschiedene Netzmodelle betrachten, die jeweils fur die Modellierung spezieller Problemkreise zweckmaBig sind. Sie hangen untereinander durch gemeinsame Interpretationsmuster zusam- men und k6nnen insgesamt als eine Methodik zur Darstellung beliebiger Systeme in beliebigen Feinheitsgraden und Ausschnitten verstanden wer- den. Die einfachen und unmittelbar einleuchtenden Prinzipien der System- modellierung mit Netzen lassen eine anschauliche Darstellung dieser Me- thodik zu, die ohne aIle Mathematik auskommt. Der Text dieses Buches ging aus Kursen hervor, die der Autor fur Projekt- ingenieure und Projektmanager aus dem Bereich rechnerintegrierter Syste- me durchgefuhrt hat. Den Teilnehmem dieser Kurse, Herm Dipl.-Ing. G. Feistl und Herm Dipl.-Ing. H. Keil von der Siemens-Schule fur Mikrocom- puter in Dusseldorf sowie Herm Prof. W. Brauer und Herm Dr. P. Schnupp sei an dieser Stelle fur zahlreiche Hinweise gedankt, Herm Dipl.-Ing. Franz Goltz fur das sorgfaltige Zeichnen der Abbildungen und dem Springer- Verlag fur die gelungene Ausstattung des Buches.

Die Informatik ist eine junge Wissenschaft, die sich durch einen rasanten technischen Fortschritt auszeichnet. Dadurch wird haufig ubersehen, dass aktuelle Themen eine teilweise lange Entwicklungsgeschichte durchlaufen haben.

Informatikprofessoren der Humboldt-Universitat zu Berlin haben zu einigen ihrer aktuellen Arbeitsgebiete die Entwicklungslinien von den Anfangen bis Gegenwart mit einem Ausblick auf die mogliche Zukunft aufgezeichnet.

Dieser spannende und lehrreiche Einblick in die Informatik offnet die Tur zu einem umfassenden und nicht nur technologisch gepragten Verstandnis."

1 d Petrinetze sind fur den Entwurf und die Analyse nicht-sequentieller (paralleler) Prozesse und Systeme geeignet. Insbesondere im Hardware- und Software-Entwurf und in der Systemspezifikation werden sie erfolgreich angewendet. Das Buch fuhrt in die grundlegenden Begriffe und Methoden des Gebietes ein. In drei Teilen werden Netze aus Bedingungen und Ereignissen, Stellen/Transitionen-Netze und schliesslich Netze mit beliebigen (individuellen) Marken behandelt. Bei den Analysemethoden werden Fakten, Synchronieabstande und Invarianten ausfuhrlich besprochen - also Methoden, die nicht auf sequentiellen Realisierungen paralleler Prozesse beruhen. Der dritte Teil behandelt den Fakten- und Invariantenkalkul fur Pradikat/Ereignis-Netze. Das Buch gibt eine geschlossene, einheitliche Darstellung der Grundbegriffe und typischen Anwendungen der Netztheorie. Es bereitet den Leser darauf vor, Petrinetze angemessen anzuwenden und die Spezialliteratur zu lesen.

Petrinetze haben sich als Modellierungstechnik fur informatikbasierte Systeme durchgesetzt. Ihre anschauliche grafische Darstellung, kombiniert mit ausdrucksstarken Analysetechniken, machen sie bei Anwendern, Studierenden und Dozenten gleichermassen beliebt.
Die Inhalte werden ausserst anschaulich dargestellt; nur zum prazisen Analysieren und Verifizieren wird formal argumentiert. Jedes Thema wird in seinem Kern behandelt; fur Varianten, Zusatze und Alternativen wird auf die Literatur verwiesen. Weitere Hinweise, Losungen der Ubungsaufgaben, Diskussionsforen etc. stehen in digitaler Form bereit."