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continued on back page ...
A. Ponse, C. Verhoef and S.F.M. van Vlijmen (Eds)
Algebra of
Communicating
Processes
Proceedings of ACP94, the First
Workshop on the Algebra of
Communicating Processes, Utrecht,
The Netherlands, 16-17 May 1994
Published in collaboration with the
British Computer Society
Springer-Verlag
London Berlin Heidelberg New York
Paris Tokyo Hong Kong
Barcelona Budapest
A. Ponse, PhD
Programming Research Group,
University of Amsterdam, Kruislaan 403,
1098 SJ Amsterdam, The Netherlands
C. Verhoef, PhD
Department of Mathematics and Computing Science,
Eindhoven University of Technology,
PO Box 513,5600 MB Eindhoven, The Netherlands
S.F.M. van Vlijmen, Drs.
Department of Philosophy,
Utrecht University, Heidelberglaan 8,
3584 CS Utrecht, The Netherlands
ISBN-13: 978-3-540-19909-0 e-ISBN-13: 978-1-4471-2120-6
DOl: 10.1007/978-1-4471-2120-6
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Apart from any fair dealing for the purposes of research or private study, or
criticism or review, as permitted under the Copyright, Designs and Patents Act
1988, this publication may only be reproduced, stored or transmitted, in any form,
or by any means, with the prior permission in writing of the publishers, or in the
case of reprographic reproduction in accordance with the terms of licences issued
by the Copyright Licensing Agency. Enquiries concerning reproduction outside
those terms should be sent to the publishers.
©British Computer Society 1995
The use of registered names, trademarks etc. in this publication does not imply,
even in the absence of a specific statement, that such names are exempt from the
relevant laws and regulations and therefore free for general use.
The publisher makes no representation, express or implied, with regard to the
accuracy of the information contained in this book and cannot accept any legal
responsibility or liability for any errors or omissions that may be made.
Typesetting: Camera ready by contributors
34/3830-543210 Printed on acid-free paper
Preface
ACP, the Algebra of Communicating Processes, is an algebraic approach
to the study of concurrent processes, initiated by Jan Bergstra and Jan
Will em Klop in the early eighties. These proceedings comprise the
contributions to ACP94, the first workshop devoted to ACP. The work-
shop was held at Utrecht University, 16-17 May 1994.
These proceedings are meant to provide an overview of current
research in the area of ACP. They contain fifteen contributions. The first
one is a classical paper on ACP by J.A. Bergstra and J.W. Klop: The
Algebra of Recursively Defined Processes and the Algebra of Regular
Processes, Report IW 235/83, Mathematical Centre, Amsterdam, 1983. It
serves as an introduction to the remainder of the proceedings and, indeed,
as a general introduction to ACP. An extended abstract of this paper is
published under the same title in the ICALP' 84 proceedings. Of the re-
maining contributions, three were submitted by the invited speakers and
the others were selected by the programme committee.
As for the presentations, Jos Baeten, Rob van Glabbeek, Jan Friso
Groote, and Frits Vaandrager were each invited to deliver a lecture. A
paper relating to Frits Vaandrager's lecture has already been submitted
for publication elsewhere and is not, therefore, included in these pro-
ceedings. Gabriel Ciobanu, one of our guests, gave an impression of his
work in an extra lecture. Furthermore, ten presentations were given on
the basis of selected papers.
The first day of ACP94 was devoted to the language .uCRL, a
formalism extending ACP with algebraic data specification, and to the
incorporation of real time in ACP. Expressiveness issues and case studies
characterized the second and last day of the workshop.
We wish to express our gratitude to the University of Amsterdam,
Utrecht University, Eindhoven University of Technology, and the
"Nationale Faciliteit Informatica" (NFl) for their financial support of
ACP94. We gratefully acknowledge the programme committee and sub-
referees for their careful reviewing. Finally, we appreciated the friendly
and smooth cooperation of all those who contributed to the preparation of
this volume.
Alban Ponse
Chris Verhoef
Bas van Vlijmen
Utrecht, July 1994
Invited Speakers
J.C.M. Baeten Eindhoven University of Technology
R.J. van Glabbeek Stanford University
J.F. Groote Utrecht University
F.W. Vaandrager CWI and University of Amsterdam
Programme Committee
1. Bethke CWI and Utrecht University
J.W. Klop CWI and Free University Amsterdam
S. Mauw Eindhoven University of Technology
J.C. Mulder Eindhoven University of Technology
A. Ponse University of Amsterdam
C. Verhoef Eindhoven University of Technology
S.F.M. van Vlijmen Utrecht University
Organizing Committee
A. Ponse University of Amsterdam
C. Verhoef Eindhoven University of Technology
S.F.M. van Vlijmen Utrecht University
Contents
The Algebra of Recursively Defined Processes and the Algebra
of Regular Processes
I.A. Bergstra and I. W. Klop .................................................. ............... .
The Syntax and Semantics of .uCRL
I.F. Groote and A. Ponse .................................................................... 26
A Correctness Proof of the Bakery Protocol in .uCRL
I.F. Groote and H. Korver .................................................................. 63
Inductive Proofs with Sets, and some Applications in Process
Algebra
I. I. van Warnel................................................. .................................... 87
Formal Semantics of Interworkings with Discrete Absolute Time
I. van den Brink and W.O.D. Griffioen ............................................ 106
The ABP and the CABP - A Comparison of Performances
in Real Time Process Algebra
I.A. Hillebrand .................................................................................. 124
Real Time Process Algebra with Infinitesimals
I.C.M. Baeten and I.A. Bergstra ...................................................... 148
On the Expressiveness of ACP (Extended Abstract)
R.I. van Glabbeek.............................................. ................................ 188
Definability with the State Operator in Process Algebra
I. Blanco................................................ ............................................. 218
Normed BPP and BPA
I. Blanco................................................ ............................................. 242
A Real Time .uCRL Specification of a System for Traffic
Regulation at Signalized Intersections
M.I. Koens and L.H. Oei ................................................................... 252
An Experiment in Implementing Process Algebra
Specifications in a Procedural Language
C. Groza ........ ... ........ ...... ....... .... .... ... ......... ... ...... ................... ..... ........ 280
Graph Isomorphism Models for Non Interleaving Process
Algebra
I. C.M. Baeten and I.A. Bergstra ...................................................... 299
Process Specification in a UNITY Format
I. I. Brunekreef............................................ ....................................... 319
x Contents
Algebraic Specification of Dynamic Leader Election
Protocols in Broadcast Networks
i.J. Brunekreef, i.-P. Katoen, R. Koymans and S. Mauw............... 338
Author Index .................................................................................... 359
The Algebra of Recursively Defined
Processes and the Algebra of Regular
Processes*
J .A. Bergstra
Programming Research Group, University of Amsterdam
Kruislaan 403, 1098 SJ Amsterdam, The Netherlands
Department of Philosophy, Utrecht University
Heidelberglaan 8, 3584 CS Utrecht, The Netherlands
J.W. Klop
Department of Software Technology, CWI
P.O. Box 94079,1090 GB Amsterdam, The Netherlands
Dept. of Mathematics and Computer Science, Free University Amsterdam
de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Abstract
We introduce recursively defined processes and regular processes, both
in presence and absence of communication. It is shown that both classes
are process algebras. An interpretation of CSP in the regular processes is
presented. As an example of recursively defined processes, bag and stack
are discussed in detail. It is shown that the bag cannot be recursively
defined without merge.
We introduce fixed point algebras which have interesting applications in
several proofs. An example is presented of a fixed point algebra which
has an undecidable word problem.
Key Words & Phrases: concurrency, nondeterministic process, merge,
process algebra, regular processes, recursively defined processes, fixed
point algebra.
Introduction
ACP, algebra of communicating processes, was introduced in BERGSTRA &
KLOP [4]. It combines a purely algebraic formulation of a part of MILNER's CCS
[13] with an algebraic presentation of the denotational semantics of processes
as given by DE BAKKER & ZUCKER in [1, 2]; moreover it includes two laws on
communication of atomic actions which are also present in HENNESSY [8].
-This is a reproduction of Report IW 235/83, Mathematisch Centrum, Amsterdam, 1983.
The authors are grateful to Wan Fokkink for organizing its conversion to a form acceptable
for the publisher. An extended abstract of this paper appeared in: J. Paredaens, editor,
Proceedings 11 th [CALP, Antwerpen, volume 172 of Lecture Notes in Computer Science,
pages 82-95. Springer-Verlag, 1984.
2
The ingredients of ACP are the following:
- A finite set A of so-called atomic actions, including a constant 8 for deadlock
(or failure). With A we denote A - {8}, the proper actions.
- A mapping. I . : A x A -+ A, called the communication function. If a I b = c
then c is the action that results from simultaneously executing a and b.
Processes will cooperate by sharing actions rather than sharing data.
- A subset H of A (usually H contains the actions which must communicate
with other actions in order to be executable). The elements of H are called
subatomic actions.
- A signature of operations ., +, II, lL ,1,8, 8H. (For x . y we will often write
xy.)
The axioms of ACP are these:
x+y=y+x Al
x + (y + z) = (x + y) + z A2
x+x=x A3
(x + y) . z = x . z + y . z A4
(x·y)·z=x·(y·z) A5
x+8=x A6
8·x = 8 A7
alb=bla CI
(a I b) I c = a I (b I c) C2
81 a = 8 C3
x II y = x lL y + y lL x + x I y CMI
alLx=a·x CM2
(ax)lLy=a(xlly) CM3
(x + y) lL z = x lL z + y lL z CM4
(ax) I b = (a I b) . x CM5
a I (bx) = (a I b) . x CM6
(ax) I (by) = (a I b) . (x II y) CM7
(x + y) I z = x I z + y I z CM8
x I (y + z) = x I y + x I z CM9
8H(a) = a if a ~ H DI
8H(a) = 8 if a E H D2
8H(x + y) = 8H(X) + 8H(Y) D3
8H(X . y) = 8H(X) ·8H(y) D4
