We present the a-calculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The calculus is an extension of the process algebra CCS, following work by Engberg and Nielsen, who added mobility to CCS while preserving its algebraic properties. The rr-calculus gains simplicity by removing all distinction between variables and constants; communication links are identified by names, and computation is represented purely as the communication of names across links. After an illustrated description of how the n-calculus generalises conventional process algebras in treating mobility, several examples exploiting mobility are given in some detail. The important examples are the encoding into the n-calculus of higher-order functions (the I-calculus and combinatory algebra), the transmission of processes as values, and the representation of data structures as processes. The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence indexed by distinctions-i.e., assumptions of inequality among names. These theories are based upon a semantics in terms of a labeled transition system and a notion of strong bisimulation, both of which are expounded in detail in a companion paper. We also report briefly on work-in-progress based upon the corresponding notion of weak bisimulation, in which internal actions cannot be observed. 0 1992 Academic Press, Inc.

A calculus of mobile processes, II

An Introduction to MultiAgent Systems.

From the Publisher:
Since the introduction of Hoares' Communicating Sequential Processes notation, powerful new tools have transformed CSP into a practical way of describing industrial-sized problems. This book gives you the fundamental grasp of CSP concepts you'll need to take advantage of those tools.Part I provides a detailed foundation for working with CSP, using as little mathematics as possible. It introduces the ideas behind operational, denotational and algebraic models of CSP. Parts II and III go into greater detail about theory and practice. Topics include: parallel operators, hiding and renaming, piping and enslavement, buffers and communication, termination and sequencing, and semantic theory. Three detailed practical case studies are also presented.For anyone interested in modeling sequential processes.

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The Theory and Practice of Concurrency

Publisher Summary
This chapter focuses on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained. As a formalism, rewrite systems have the full power of Turing machines and may be thought of as nondeterministic Markov algorithms over terms rather than strings. The theory of rewriting is in essence a theory of normal forms. To some extent, it is an outgrowth of the study of A. Church's Lambda Calculus and H. B. Curry's Combinatory Logic. The chapter discusses the syntax and semantics of equations from the algebraic, logical, and operational points of view. To use a rewrite system as a decision procedure, it must be convergent. The chapter describes this fundamental concept as an abstract property of binary relations. To use a rewrite system for computation or as a decision procedure for validity of identities, the termination property is crucial. The chapter presents the basic methods for proving termination. The chapter discusses the question of satisfiability of equations and the convergence property applied to rewriting.

CHAPTER 6 – Rewrite Systems

We survey the literature available on the topic of domain-specific languages as used for the construction and maintenance of software systems. We list a selection of 75 key publications in the area, and provide a summary for each of the papers. Moreover, we discuss terminology, risks and benefits, example domain-specific languages, design methodologies, and implementation techniques.

https://people.cis.ksu.edu/~schmidt/505f14/Lectures/DSLbib.pdf

Domain-specific languages: an annotated bibliography

Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite system behind the communication algebra is shown to be confluent and terminating (modulo its permutative reductions). Further, some relationships are shown to hold between the four concepts of merging. © 1984 Academic Press, Inc.

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Process algebra for synchronous communication

Preface (Bergstra, Ponse, Smolka). Part 1: Basic Theory. The linear time - brancing time spectrum I (Van Glabbeek). Trace-oriented models of concurrency (Broy, Olderog). Structural operational semantics (Aceto, Fokkink, Verhoef). Modal logics and mu-calculi: an intorduction (Bradfield, Stirling). Part 2: Finite-State Processes. Process algebra with recursive operations (Bergstra, Fokkink, Ponse). Equivalence and preorder checking for finite-state systems (Cleaveland, Sokolsky). Part 3: Infinite-State Processes. A symbolic approach to value-passing processes (Ingolfsdottir, Lin). An introduction to the pi-calculus (Parrow). Verification on infinite structures (Bukart, Caucal, Moller, Steffen). Part 4: Extensions. Process algebra with timing: real time and discrete time (Baeten, Middelburg). Probabilistic extensions of process algebras (Jonsson, Larsen, Yi). Priority in process algebra (Cleaveland, Luettgen, Natarajan). Part 5: Non-Interleaving Process Algebra. Partial-order process algebra (Baeten, Basten). A unified model for nets and process algebras (Best, Devillers, Koutny). Process algebras with localities (Castellani). Action refinement (Gorrieri, Rensink). Part 6: Tools and Applications. Algebraic process vertification (Groote, Reniers). Discrete time process algebra and the semantics of SDL (Bergstra, Middelburg, Usenko). A process algebra for Interworkings (Mauw, Reniers).

Handbook of Process Algebra

We present an axiom system ACP, for communicating processes with silent actions (‘τ-steps’). The system is an extension of ACP, Algebra of Communicating Processes, with Milner's τ-laws and an explicit abstraction operator. By means of a model of finite acyclic process graphs for ACPτ, syntactic properties such as consistency and conservativity over ACP are proved. Furthermore, the Expansion Theorem for ACP is shown to carry over to ACPτ. Finally, termination of rewriting terms according to the ACPτ, axioms is probed using the method of recursive path orderings.

Algebra of communicating processes with abstraction

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.

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Real time process algebra

This paper is concerned with finding complete axiomatizations of probabilistic processes. We examine this problem within the context of the process algebra ACP and obtain as our end-result the axiom system prACP I −- , a probabilistic version of ACP which can be used to reason algebraically about the reliability and performance of concurrent systems. Our goal was to introduce probability into ACP in as simple a fashion as possible. Optimally, ACP should be the homomorphic image of the probabilistic version in which the probabilities are forgotten.

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Jan A. Bergstra

Papers

Process algebra for synchronous communication

Handbook of Process Algebra

Algebra of communicating processes with abstraction

Real time process algebra

Axiomatizing probabilistic processes: ACP with generative probabilities