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 model micro-architectures with non-pipelined instruction processing and pipelined instruction processing using Maurer machines, basic thread algebra and program algebra. We show that stored programs are executed as intended with these micro-architectures. We believe that this work provides a new mathematical approach to the modelling of micro-architectures and the verification of their correctness and the anticipated speed-up results.

Maurer computers for pipelined instruction processing

Promise Theory bridges the worlds of semantics and dynamics to describe interactions between autonomous agencies within a system. It provides a semi-formal language for modelling intent and its outcome, which results in a chemistry for cooperative behaviour. This book is aimed at scientists and engineers. It introduces readers to promises in a practical manner, keeping within the paradigm of `voluntary cooperation'. The book draws on examples from the real world, with a special emphasis on computers and information systems.

Promise Theory: Principles and Applications

We investigate conditional expressions in the setting of ACP, an algebraic theory about processes. We introduce ACPc, an extension of ACP with conditional expressions in which the conditions are taken from a free Boolean algebra over a set of generators, and also its main models, called full splitting bisimilation models. We add two simple mechanisms for condition evaluation to ACPc; and we show their connection with state operators and signal emission, mechanisms from other extensions of ACP usable for condition evaluation. To allow for looking back on conditions under which preceding actions have been performed, we add a retrospection operator on conditions to ACPc. The choice of conditions forces us to introduce a new variant of bisimulation. However, without the generality implied by that choice, it would not have been possible to extend ACPc with retrospection. The addition of retrospection is a basic way to increase expressiveness.

Splitting bisimulations and retrospective conditions

Call a set of assertions A complete (with respect to a class of programs S ) if for any p , q∈ A and S∈ S , wherever { p } S { q } holds, then all intermediate assertions can be chosen from A . This paper is devoted to the study of the problem which sets of assertions are complete in the above sense. We prove that any set of recursive assertions containing true and false is not complete. We prove the completeness for while programs of some more powerful assertions, e.g. the set of recursively enumerable assertions. Finally, we show that by allowing the use of an ‘auxilliary’ coordinate, the set of recursive assertions is complete for while programs.

Recursive assertions are not enough, or are they?

http://staff.science.uva.nl/~alban/publist/ipl.pdf

Jan A. Bergstra

Papers

Maurer computers for pipelined instruction processing

Promise Theory: Principles and Applications

Splitting bisimulations and retrospective conditions

Recursive assertions are not enough, or are they?

Kleen's three-valued logic and process algebra