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.

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.

Concurrent systems are generally understood in terms of behavioral notions. Models for Concurrency analyzes the subject in terms of events and their temporal relationship rather than on global states. It presents a comprehensive analysis of model theory applied to concurrent protocols, and seeks to provide a theory of concurrency that is both intuitively appealing and rigorously based on mathematical foundations. The book is divided into three main sections. The first introduces the required concepts from model theory, details the structures that are used to model concurrency, gives an in-depth description and explanation of the semantics of a simple language that allows concurrent execution of sequential programs, and deals with the question of resolving executions into higher-level and lower-level granularities. The second and third sections apply the theory developed to practical examples, and an exposition of the producer/consumer problem with details of two solutions is given. The author also deals with message passing, as opposed to shared memory.

Intheworldweliveinconcurrencyisthenorm.Forexample,thehumanbody isamassivelyconcurrentsystem,comprisingahugenumberofcells,allsim- taneously evolving and independently engaging in their individual biological processing.Inaddition,inthebiologicalworld,trulysequentialsystemsrarely arise. However, they are more common when manmade artefacts are cons- ered. In particular, computer systems are often developed from a sequential perspective. Why is this? The simple reason is that it is easier for us to think about sequential, rather than concurrent, systems. Thus, we use sequentiality as a device to simplify the design process. However, the need for increasingly powerful, ?exible and usable computer systems mitigates against simplifying sequentiality assumptions. A good - ample of this is the all-powerful position held by the Internet, which is highly concurrent at many di?erent levels of decomposition. Thus, the modern c- puter scientist (and indeed the modern scientist in general) is forced to think aboutconcurrentsystemsandthesubtleandintricatebehaviourthatemerges from the interaction of simultaneously evolving components. Over a period of 25 years, or so, the ?eld of concurrency theory has been involved in the development of a set of mathematical techniques that can help system developers to think about and build concurrent systems. These theories are the subject matter of this book.

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.