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.

/pdf/the-theory-and-practice-of-concurrency-1kzi2sg7cs.pdf

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

We present a process algebra based approach to formalize the interactions of computing devices such as the representation of policies and the resolution of conflicts. As an example we specify how promises may be used in coming to an agreement regarding a simple though practical transportation problem.

A process algebra based framework for promise theory

The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability theory are restated in this framework.

Signed Meadow Valued Probability Functions

Parallel composition in a static setting introduces algebra, in the form of static process algebra, as a modelling tool at the level of primary school mathematics Static process algebra may play the role of a prearithmetic algebra Multi-dimensional counters can be used to measure the number of components in a static process expression

/pdf/static-process-algebra-as-pre-arithmetical-content-for-116nv55kla.pdf

Jan A. Bergstra

Papers

A process algebra based framework for promise theory

Signed Meadow Valued Probability Functions

Static Process Algebra as Pre-arithmetical Content for School Arithmetic

The Equational Specification of Finite Minimal Unoids Using only Unary Hidden Functions

Conditional rewrite rules; confluency and termination : Preprint