A calculus of mobile processes, I

Abstract

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.

Modal characterization of weak bisimulation for higher-order processes

“…However, first-order process calculi are limited in the sense that they assume a fixed interconnection structure between the processes involved. Recently, name-passing and higher-order calculi have been proposed to remedy this obvious deficiency [10,15]. They allow the communication of processes and functions, and thus support a powerful abstraction technique which is similar to the one found in higher-order programming languages and caters for systems with changing interconnection structure.…”

On the Concurrency of Inter-organizational Business Processes

“…A distinctive feature of π-calculus when compared to earlier process algebras is the concept of mobility, which is intended to allow π-calculus to model processes with changing structure [27]. Basically, mobility involves the ability to send links through links.…”

How reliable is satellite navigation for aviation? Checking availability properties with probabilistic verification

“…Because of the detailed nature of the model and the corresponding state space size, we first consider a small number of satellites (N=4, 5,6,7,8). It is possible, though, that availability properties analysed in these small models will also be exhibited by a more laege size (e.g., 17 satellites).…”

“…Properties of the modelled system can be verified by studying the underlying labelled transition system. For this purpose, we specify the underlying models using the probabilistic π-calculus, an extension of the π-calculus [7,8] for modelling mobile systems.…”