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Process algebra is a widely accepted and much used technique in the specification and verification of parallel and distributed software systems. This book sets the standard for the field. It assembles the relevant results of most process algebras currently in use, and presents them in a unified framework and notation. The authors describe the theory underlying the development, realization and maintenance of software that occurs in parallel or distributed systems. A system can be specified in the syntax provided, and the axioms can be used to verify that a composed system has the required external behavior. As examples, two protocols are completely specified and verified in the text: the Alternating-Bit communication Protocol, and Fischer's Protocol of mutual exclusion. The book serves as a reference text for researchers and graduate students in computer science, offering a complete overview of the field and referring to further literature where appropriate.

This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched.

Abstract.We describe an axiom system ACPp that incorporates real timed actions. Many examples are provided in order to explain the intuitive contents of the notation. ACPp is a generalisation of ACP. This implies that some of the axioms have to be relaxed and that ACP can be recovered as a special case from it. The purpose of ACPp is to serve as a specification language for real time systems. The axioms of ACPp explain its operational meaning in an algebraic form.

We construct a graph model for ACP"' the algebra of communicating processes with silent steps, in which Koomen's Fair Abstraction Rule (KFAR) holds, and also versions of the Approximation Induction Principle (AIP) and the Recursive Definition & Specification Principles (RDP&RSP). We use this model to prove that in ACP" (but not in ACP!) each computably recursively definable process is finitely recursively definable.