Process Algebra: Equational Theories of Communicating Processes

Abstract

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.

Avoiding diamonds in desynchronisation

“…[16]). We do not fix a set of desirable properties a priori, but rather aim for desynchronisability modulo a behavioural equivalence that preserves a large set of possibly desirable properties.…”

“…We model this observation by a predicate, called empty-buffer predicate. Now by enriching the transfer condition of branching bisimilarity (just like how the termination predicate is handled in the definition of branching bisimulation; see [16]) we ensure that an asynchronous system constructed from a desynchronisable synchronous system has the following communication property: "every sent message is eventually received". Note that this property was already present in the previous works [3,8,9] on desynchronisability; although, it was never made explicit with the respective equivalences studied previously.…”

“…The notation p s denotes the synchronous composition of processes p and s. Note that one can construct the synchronous composition of processes, say p and p s, by renaming the synchronous interaction (e.g. the renaming operator from TCP process algebra [16]) of p s into a send message or receive message …”

“…Subsequently, we define branching bisimulation (see [16,17]) as an equivalence between processes that abstracts from internal actions. In Subsection 5.1, we discuss the impact of alternative choices of abstraction schemes on desynchronisability modulo branching bisimulation.…”

“…[16]. Here, we interpret Condition 2 (likewise Condition 4) as follows: if two processes q, q are branching bisimilar and q has empty buffer, then q can empty its buffer contents by performing invisible actions and become branching bisimilar to q.…”