Browse Books

Reviewer: Stephen D. Wolthusen

Algebraic approaches to modeling, specifying, and reasoning over programs, particularly concurrent processes, have been the subject of scientific inquiry for more than two decades. Besides communicating sequential processes introduced by Hoare [1] and the calculus of communicating systems introduced by Milner [2], the third major strand of research on algebraic approaches to concurrency is the algebra of communicating processes (ACP) by Bergstra and Klop. While a number of books on process algebra exist, thus far, the concise presentation of process algebra that includes timing issues has been limited to a handbook article [3] by the authors of this book. This makes the volume a welcome addition to researchers interested in algebraic approaches to processes and academics that are preparing advanced courses on the subject. Several variants of process algebra with timing are covered in the book, which is written in a highly structured approach, permitting quick reviews of a specific area of interest, albeit at the price of some redundancy in the presentation. The book starts with a somewhat informal review of ACP without timing that should be augmented by a more precise presentation, such as that seen in Fokkink [4] or Baeten and Weijland [5], for use in class. This chapter is divided into a presentation of basic process algebra and a discussion of the algebra of communicating processes, building on the process algebra of the preceding section. This organization is maintained for other chapters as well. Also recurring throughout the book is a structure that first informally introduces concepts and pragmatics of the theory to be presented, followed by a more formal discussion. Chapters 2 through 5 introduce a number of timed process algebra frameworks, beginning with discrete relative timing models in chapter 2. While the presentation in the chapter itself is at times somewhat informal, soundness and completeness proofs are given in an appendix. The application areas of the extended process algebra are then covered by examples that can be modeled by ACP with discrete relative timing, while a summary section discusses the relationship of the extension to basic ACP. Chapter 3 then proceeds to extend ACP by introducing a model of discrete absolute timing where actions and time are separated, also introducing the concept of discrete initial abstraction for parametric timing. Continuous timing is the subject of chapters 4 and 5; the presentation follows the general outline described above, with chapter 4 discussing continuous relative timing, and chapter 5 covering continuous absolute timing. As with chapter 2, these chapters all include exercises demonstrating the applicability of the extended models. Chapter 6 discusses the concept of abstraction in process algebra for each of the frameworks introduced in chapters 1 through 5. As before, each of the (somewhat brief) frameworks is covered by a discussion of the applicable basic process, as well as a section on the relevant algebra of communicating processes, and includes a brief example of the use of abstraction. Chapter 7 then concludes the body of the book with several additions to the ACP framework with continuous absolute timing and integration. These operators include a state operator to represent the execution of a process in a state, the maximal progress operator to express the execution of actions that are to take place as soon as possible, and a process creation operator that permits the modeling of starting a concurrent process by another process. Appendix A expands the discussion of soundness and completeness in ACP with discrete relative timing covered in chapter 2. Appendix B covers additional background material, including equational logic and structural operational semantics, although the latter is treated rather briefly and should be augmented by additional material such as Aceto et al. [6]. Considerable numbers of exercises throughout the book, as well as meaningful examples, round it out, making it highly suitable for use in advanced classes. Online Computing Reviews Service