Joachim Parrow

A calculus of mobile processes, I

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

This is the second of two papers in which we present the rc-calculus, a calculus of mobile processes. The companion paper (Milner, Parrow, and Walker, 1989a) contains an introduction to the calculus through a sequence of examples, together with statements of many results about it. The purpose of the present paper is to provide a detailed presentation of some of the theory of the calculus developed to date, and in particular to establish most of the results stated in the companion paper. Once the motivation and intuition for the n-calculus are understood, with the help of the companion paper, the present paper serves as a self-contained development of the theory. To achieve this we have found it necessary to repeat some material from the companion paper. Section 1 contains a description of the syntax of agents and a discursive presentation of the transitional semantics. In Section 2 we present and motivate the definitions of strong bisimulation and strong bisimilarity, strong equivalence, and a useful family of indexed equivalences. Section 3 contains a series of properties of strong bisimilarity, while properties of

The concurrency workbench: a semantics-based tool for the verification of concurrent systems

The Concurrency Workbench is an automated tool for analyzing networks of finite-state processes expressed in Milners Calculus of Communicating Systems. Its key feature is its breadth: a variety of different verification methods, including equivalence checking, preorder checking, and model checking, are supported for several different process semantics. One experience from our work is that a large number of interesting verification methods can be formulated as combinations of a small number of primitive algorithms. The Workbench has been applied to the verification of communications protocols and mutual exclusion algorithms and has proven a valuable aid in teaching and research.

The fusion calculus: expressiveness and symmetry in mobile processes

We present the fusion calculus as a significant step towards a canonical calculus of concurrency. It simplifies and extends the /spl pi/-calculus. The fusion calculus contains the polyadic /spl pi/-calculus as a proper subcalculus and thus inherits all its expressive power. The gain is that fusion contains actions akin to updating a shared state, and a scoping construct for bounding their effects. Therefore it is easier to represent computational models such as concurrent constraints formalisms. It is also easy to represent the so called strong reduction strategies in the /spl lambda/-calculus, involving reduction under abstraction. In the /spl lambda/-calculus these tasks require elaborate encodings. Our results on the fusion calculus in this paper are the following. We give a structured operational semantics in the traditional style. The novelty lies in a new kind of action, fusion actions for emulating updates of a shared state. We prove that the calculus contains the /spl pi/-calculus as a subcalculus. We define and motivate the bisimulation equivalence and prove a simple characterization of its induced congruence, which is given two versions of a complete axiomatization for finite terms. The expressive power of the calculus is demonstrated by giving a straight-forward encoding of the strong lazy /spl lambda/-calculus, which admits reduction under /spl lambda/ abstraction.

Modal logics for mobile processes

In process algebras, bisimulation equivalence is typically defined directly in terms of the operational rules of action; it also has an alternative characterisation in terms of a simple modal logic (sometimes calledHennessy-Milner logic . This paper first defines two forms of bisimulation equivalence for the\031-calculus , a process algebra which allows dynamic reconfiguration among processes; it then explores a family of possible logics, with different modal operators. It is proven that two of these logics characterise the two bisimulation equivalences. Also, the relative expressive power of all the logics is exhibited as a lattice.

The concurrency workbench

The Concurrency Workbench is an automated tool that caters for the analysis of networks of finite-state processes expressed in Milners Calculus of Communicating Systems. Its key feature is its scope: a variety of different verification methods, including equivalence checking, preorder checking, and model checking, are supported for several different process semantics. One experience from our work is that a large number of interesting verification methods can be formulated as combinations of a small number of primitive algorithms. The Workbench has been applied to examples involving the verification of communications protocols and mutual exclusion algorithms and has proven a valuable aid in teaching and research.

An Introduction to the π-Calculus

Abstract The π-calculus is a process algebra where processes interact by sending communication links to each other. This paper is an overview of and introduction to its basic theory. We explore the syntax, semantics, equivalences and axiomatizations of the most common variants.

An algebraic verification of a mobile network

In a mobile communication network some nodes change locations, and are therefore connected to different other nodes at different points in time. We show how some important aspects of such a network can be formally defined and verified using theπ-calculus, which is a development of CCS (Calculus of Communicating Systems) allowing port names to be sent as parameters in communication events. As an example of a mobile network we consider the Public Land Mobile Network currently being developed by the European Telecommunication Standards Institute and concentrate on the handover procedure which controls the dynamic topology of the network.

Submodule construction as equation solving in CCS

Abstract In top-down design methodologies the following problem arises: given specifications of a system and some of its submodules, derive a specification for the remaining submodules. We formulate this problem in CCS as an equation (A|X)⧹L ≈ B, where X is unknown, B represents the whole system, A the known submodules, and L the channels over which the submodules interact. We present a procedure for solving such equations by successive transformation of equations into simpler equations in parallel with generation of a solution. The procedure has been implemented as a semiautomatic program, where the user may interact in order to guide the transformations towards particular solutions. As an example we demonstrate the automatic generation of receivers of two versions of the Alternating Bit protocol.

Deciding Bisimulation Equivalences for a Class of Non-Finite-State Programs

Traditionally, many automatic program verification techniques have been applicable only to finite-state programs. In this paper we extend some of these techniques to a class of infinite-state programs that, in addition to having a finite-state control component, may read, store, and write but not perform any other computations on data. Such programs are data-independent in the sense that their behavior does not depend on the actual data values supplied. We consider the problems of deciding strong equivalence and observation equivalence, defined by bisimulations (as in CCS), between such programs. These equivalences have major applications in verification of communication protocols. We present reductions of these problems to the problem of deciding strong equivalence and observation equivalence between finite-state programs, for which polynomial time algorithms exist. The equivalence problems on data-independent programs are shown to be NP-hard in the size of the programs.