The theory of Petri nets is a part of computer science whose importance is increasingly acknowledged. Many papers and anthologies, whose subject matter is net theory and its applications, have appeared to date. There exist at least seven introductory textbooks on the theory. The present monograph augments this literature by offering a mathematical treatment of one of the central aspects of net theory: the modelling of concur rency by partially ordered sets. Occurrence nets - which are special nets as well as special partial orders - are proposed by net theory for this purpose. We study both the general properties of occurrence nets and their use in describing the concurrent behaviour of systems. Occurrence nets may be contrasted with a more language-oriented approach to the modelling of concurrency known as arbitrary interleaving. We will dis cuss some connections between these' two approaches. Other approaches based on partially ordered sets - such as the theory of traces, the theory of event structures and the theory of semi words - are not considered in this book, in spite of the strong links between them and net theory.

Autorentext

Eike Best Born in 1951 in Germany, graduated in Informatik in 1974 at the Technische Hochschule Karlsruhe. He has joined projects led by Peter Lauer and Brian Randell at the University of Newcastle upon Tyne (1975-1981) where he started to cooperate with Raymond Devillers. He earned his PhD in 1982 at Newcastle and a Habilitation degree at the University of Bonn in 1988 while working at Carl Adam Petri's Institute. He has taught a range of computer science courses as a professor in Paderborn, Hildesheim, and Oldenburg (from 1996), and he has a research and project leadership record, with an emphasis on semantics and Petri nets. Raymond Devillers Born in 1945 in Belgium, graduated in Mathematics and Physics, he got a PhD Thesis in 1974 on the use of games for deadlock prevention at the University of Brussels. During a postdoctorate stay in Newcastle upon Tyne, he met Eike Best, start of a long-lasting cooperation. After a job at the Computer Center of the ULB, he started a professorial career at the same university, where he taught many different courses in practical and theoretical computer sciences. He conducted many researches, in particular about the analysis and synthesis of Petri nets, before and after his retirement in 2010.

Klappentext

The theory of the processes of concurrent systems is studiedusing partiallyordered sets. The study is based on Petrinet theory. General properties of posets and their relationswith properties of concurrent systems are examined.

Inhalt
1 Introduction.- 2 Partially Ordered Sets.- 2.1 Introduction and Basic Definitions.- 2.2 Combinatorialness and Discreteness.- 2.3 N-density and K-density.- 2.4 D-continuity.- 2.5 Occurrence Posets.- 3 Petri Nets.- 3.1 Nets and Markings.- 3.2 Transition Rule and Occurrence Sequences.- 3.3 Occurrence Nets and Processes.- 3.4 Inductive Definition of Processes.- 3.5 Systems of Finite Synchronisation.- 4 Connections Between Systems and Processes.- 4.1 Introduction.- 4.2 K-density and Safeness.- 4.3 D-continuity and Frozen Tokens.- 4.4 A Closing Remark on Finite 1-safe Nets.- Bibliographical Notes.- Notation and Terminology.- Index of Definitions.