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Paradigms of Concurrency: Observations, Behaviours, and Systems - a Petri Net View - Ryszard Janicki (McMaster University, CA) Jetty Kleijn (Leiden University, NL) Maciej Koutny (Newcastle University, UK) Lukasz Mikulski (Nicolaus Copernicus University, PL) Concurrency can be studied at different yet consistent levels of abstraction: from individual behavioural observations via more abstract concurrent histories that can be represented by causality structures capturing invariant dependencies between executed actions, to system level constructs such as Petri nets or process algebra expressions. Histories can then be understood as sets of closely related observations. Depending on the nature of the observed relationships between executed actions involved in a single concurrent history, one may identify different concurrency paradigms underpinned by different kinds of causality structures such as partial orders. This book studies fundamental mathematical abstractions to capture and relate observations, histories, and systems. In particular, taking a Petri net view, we present system models fitting various concurrency paradigms and their associated causality structures.

Auf dem Gebiet der Petri-Netze und Vektoradditionssysteme sind viele Entscheidungsfragen ungeklärt, die Uli Schlachter in seiner Masterarbeit motiviert haben, Spiele auf sogenannten Spielstrukturen mit einer ähnlichen Semantik zu untersuchen. Hierbei handelt es sich um eine Art von Zwei-Spieler-Spielen auf einem gerichteten Graphen. Der Autor erarbeitet verschiedene Gewinnbedingungen und zeigt ihre Entscheidbarkeit. Die Arbeit beleuchtet diese Themen spieltheoretisch, bietet aber auch eine exemplarische Anwendung verschiedener Aspekte der Spieltheorie.

Hardware Design and Petri Nets presents a summary of the state of the art in the applications of Petri nets to designing digital systems and circuits. The area of hardware design has traditionally been a fertile field for research in concurrency and Petri nets. Many new ideas about modelling and analysis of concurrent systems, and Petri nets in particular, originated in theory of asynchronous digital circuits. Similarly, the theory and practice of digital circuit design have always recognized Petri nets as a powerful and easy-to-understand modelling tool. The ever-growing demand in the electronic industry for design automation to build various types of computer-based systems creates many opportunities for Petri nets to establish their role of a formal backbone in future tools for constructing systems that are increasingly becoming distributed, concurrent and asynchronous. Petri nets have already proved very effective in supporting algorithms for solving key problems in synthesis of hardware control circuits. However, since the front end to any realistic design flow in the future is likely to rely on more pragmatic Hardware Description Languages (HDLs), such as VHDL and Verilog, it is crucial that Petri nets are well interfaced to such languages. Hardware Design and Petri Nets is divided into five parts, which cover aspects of behavioral modelling, analysis and verification, synthesis from Petri nets and STGs, design environments based on high-level Petri nets and HDLs, and finally performance analysis using Petri nets. Hardware Design and Petri Nets serves as an excellent reference source and may be used as a text for advanced courses on the subject.

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 keyproperties 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.

This monograph presents a comprehensive introduction to timed automata (TA) and time Petri nets (TPNs) which belong to the most widely used models of real-time systems. Some of the existing methods of translating time Petri nets to timed automata are presented, with a focus on the translations that correspond to the semantics of time Petri nets, associating clocks with various components of the nets.'Advances in Verification of Time Petri Nets and Timed Automata – A Temporal Logic Approach'introduces timed and untimed temporal specification languages and gives model abstraction methods based on state class approaches for TPNs and on partition refinement for TA. Moreover, the monograph presents a recent progress in the development of two model checking methods, based on either exploiting abstract state spaces or on application of SAT-based symbolic techniques. The book addresses research scientists as well as graduate and PhD students in computer science, logics, and engineering of real time systems.

Foundation of logic historically dates back to the times of Aristotle, who pioneered the concept of truth/falsehood paradigm in reasoning. Mathematical logic of propositions and predicates, which are based on the classical models of Aristotle, underwent a dramatic evolution during the last 50 years for its increasing applications in automated reasoning on digital computers. The subject of Logic Programming is concerned with automated reasoning with facts and knowledge to answer a user's query following the syntax and semantics of the logic of propositions/predicates. The credit of automated reasoning by logic programs goes to Professor Robinson for his well-known resolution theorem that provides a general scheme to select two program clauses for deriving an inference. Until now Robinson's theorem is being used in PROLOG/DATALOG compilers to automatically build a Select Linear Definite (SLD) clause based resolution tree for answering a user's query. The SLD-tree based scheme for reasoning undoubtedly opened a new era in logic programming for its simplicity in implementation in the compilers. In fact, SLD-tree construction suffices the need for users with a limited set of program clauses. But with increase in the number of program clauses, the execution time of the program also increases linearly by the SLD-tree based approach. An inspection of a large number of logic programs, however, reveals that more than one pair of program clauses can be resolved simultaneously without violating the syntax and the semantics of logic programming. This book employs this principle to speed up the execution time of logic programs.

Petri nets do not designate a single modeling formalism. In fact, newcomers to the field confess sometimes to be a little puzzled by the diversity of formalisms that are recognized under this'umbrella'. Disregarding some extensions to the theoretical modeling capabilities, and looking at the level of abstraction of the formalisms, Condition/Event, Elementary, Place/Transition, Predicate/Transition, Colored, Object Oriented... net systems are frequently encountered in the literature. On the other side, provided with appropriate interpretative extensions, Controled Net Systems, Marking Diagrams (the Petri net generalization of State Diagrams), or the many-many variants in which time can be explicitly incorporated -Time(d), Deterministic, (Generalized) Stochastic, Fuzzy...- are defined. This represents another way to define practical formalisms that can be obtained by the'cro- product'of the two mentioned dimensions. Thus Petri nets constitute a modeling paradigm, understandable in a broad sense as'the total pattern of perceiving, conceptualising, acting, validating and valuing associated with a particular image of reality that prevails in a science or a branch of science'(Thomas S. Kuhn).