This volume contains the proceedings of the 1990 Spring School of Theoretical Computer Science, devoted to the semantics of concurrency. The papers are of two kinds: - surveys and tutorials introducing the subject to novices and students and giving updates of the state of the art, - research papers presenting recent achievements in the semantics of concurrency. The contributions explicate the connections, similarities and differences between various approaches to the semantics of concurrency, such as pomsets and metric semantics, event structures, synchronization trees, fixpoints and languages, traces, CCS and Petri nets, and categorical models. They also cover and compare the various notions of observation and bisimulation equivalences, logics for concurrency, and applications to dis- tributed systems.

The author presents a theory of concurrent processes where three different semantic description methods that are usually studied in isolation are brought together. Petri nets describe processes as concurrent and interacting machines; algebraic process terms describe processes as abstract concurrent processes; and logical formulas specify the intended communication behaviour of processes. At the heart of this theory are two sets of transformation rules for the top-down design of concurrent processes. The first set can be used to transform stepwise logical formulas into process terms, whilst process terms can be transformed into Petri nets by the second set. These rules are based on novel techniques for the operational and denotational semantics of concurrent processes. Various results and relationships between nets, terms and formulas starting with formulas and illustrated by examples. The use of transformations is demonstrated in a series of case studies, and the author also identifies directions for research.

The semantics of concurrent systems is one of the most vigorous areas of research in theoretical computer science, but suffers from disagree ment due to different, and often incompatible, attitudes towards abstracting non-sequential behaviour. When confronted with process algebras, which give rise to very elegant, highly abstract and com positional models, traditionally based on the interleaving abstraction, some argue that the wealth of contribution they have made is partially offset by the difficulty in dealing with topics such as faimess. On the other hand, the non-interleaving approaches, based on causality, although easing problems with fairness and confusion, still lack struc ture, compositionality, and the elegance of the interleaving counter parts. Since both these approaches have undoubtedly provided important contributions towards understanding of concurrent systems, one should concentrate on what they have in common, rather than the way they differ. The Intemational Workshop on Semantics for Concurrency held at the University of Leicester on 23-25 July 1990 was organised to help overcome this problem. Its main objective was not to be divisive, but rather to encourage discussions leading towards the identification of the positive objective features of the main approaches, in the hope of furthering common understanding. The Workshop met with an excel lent response, and attracted contributions from all over the world. The result was an interesting and varied programme, which was a combi nation of invited and refereed papers. The invited speakers were: Prof. dr. E. Best (Hildesheim University) Prof. dr. A.

CSP notation has been used extensively for teaching and applying concurrency theory, ever since the publication of the text Communicating Sequential Processes by C.A.R. Hoare in 1985. Both a programming language and a specification language, the theory of CSP helps users to understand concurrent systems, and to decide whether a program meets its specification. As a member of the family of process algebras, the concepts of communication and interaction are presented in an algebraic style. An invaluable reference on the state of the art in CSP, Understanding Concurrent Systems also serves as a comprehensive introduction to the field, in addition to providing material for a number of more advanced courses. A first point of reference for anyone wanting to use CSP or learn about its theory, the book also introduces other views of concurrency, using CSP to model and explain these. The text is fully integrated with CSP-based tools such as FDR, and describes how to create new tools based on FDR. Most of the book relies on no theoretical background other than a basic knowledge of sets and sequences. Sophisticated mathematical arguments are avoided whenever possible. Topics and features: presents a comprehensive introduction to CSP; discusses the latest advances in CSP, covering topics of operational semantics, denotational models, finite observation models and infinite-behaviour models, and algebraic semantics; explores the practical application of CSP, including timed modelling, discrete modelling, parameterised verifications and the state explosion problem, and advanced topics in the use of FDR; examines the ability of CSP to describe and enable reasoning about parallel systems modelled in other paradigms; covers a broad variety of concurrent systems, including combinatorial, timed, priority-based, mobile, shared variable, statecharts, buffered and asynchronous systems; contains exercises and case studies to support the text; supplies further tools and information at the associated website: http://www.comlab.ox.ac.uk/ucs/. From undergraduate students of computer science in need of an introduction to the area, to researchers and practitioners desiring a more in-depth understanding of theory and practice of concurrent systems, this broad-ranging text/reference is essential reading for anyone interested in Hoare’s CSP.

The cooperation test [Apt, Francez & de Roever] was originally conceived to capture the proof theoretical analogue of distributed message exchange between disjoint processes, as opposed to the interference freedom test [Owicki & Gries], being the proof theoretical analogue of concurrent communication by means of interference through jointly shared variables. Some authors ([Levin & Gries, Lamport & Schneider, Schlichting and Schneider]) stress that both forms of communication can be proof theoretically characterized using interference freedom only, since proofs for both ultimately amount to an invariance proof of a big global assertion [Ashcroft], invariance of whose parts amounts to interference freedom. Yet I feel that the characteristic nature of the cooperation test is still preserved in the analysis of these authors, because in their analysis of CSP the part dealing with interference freedom specializes to maintenance of a global invariant, the expression of which requires per process the introduction of auxiliary variables which are updated in that process only, thus preserving the concept of disjointness (as opposed to sharing), since now all variables from different processes are disjoint. The cooperation test has been applied to characterize concurrent communication as occurring in Hoare's Communicating Sequential Processes (CSP) [Hoare 2], Ichbiah's ADA [ARM], and Brinch Hansen's Distributed Processes (DP) [Brinch Hansen]. This characterization has been certified through soundness and completeness proofs [Apt 2, Gerth]. As in the interference freedom test this characterization consists of two stages, a local sequential stage and a global stage.

This collection of reprints describes a unified treatment of semantics, covering a wide range of notions in parallel languages. Included are several foundational and introductory papers developing the methodology of metric semantics, studies on the comparative semantics of parallel object-oriented and logic programming, and papers on full abstraction and transition system specifications. In addition, links with process algebra and the theory of domain equations are established. Throughout, a uniform proof technique is used to relate operational and denotational models. The approach is flexible in that both linear time, branching time (or bisimulation) and intermediate models can be handled, as well as schematic and interpreted elementary actions. The reprints are preceded by an extensive introduction surveying related work on metric semantics.

"This book discusses the semantic foundations of concurrent systems with nondeterministic and probabilistic behaviour. Particular attention is given to clarifying the relationship between testing and simulation semantics and characterising bisimulations from metric, logical, and algorithmic perspectives. Besides presenting recent research outcomes in probabilistic concurrency theory, the book exemplifies the use of many mathematical techniques to solve problems in computer science, which is intended to be accessible to postgraduate students in Computer Science and Mathematics. It can also be used by researchers and practitioners either for advanced study or for technical reference"--Jacket.