The Space and Motion of Communicating Agents

215 Pages·2009·2.12 MB·English

by  Robin Milner

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THE SPACE AND MOTION OF
COMMUNICATING AGENTS
Theworldisincreasinglypopulatedwithinteractiveagentsdistributedinspace,real
or abstract. These agents can be artificial, as in computing systems that manage
andmonitortrafficorhealth;ortheycanbenatural,e.g. communicatinghumans,
orbiologicalcells. Itisimportanttobeabletomodelnetworksofagentsinorder
tounderstandandoptimisetheirbehaviour. RobinMilner’spurposeistodescribe
inthisbookjustsuchamodel,andhedoessobypresentingaunifiedandrigorous
structuraltheory,basedonbigraphs,forsystemsofinteractingagents. Thistheory
isabridgebetweentheexistingtheoriesofconcurrentprocessesandtheaspirations
forubiquitoussystems,whoseenormoussizechallengesourunderstanding.
Thebookbeginswithanassessmentoftheproblemsthatastructuralmodelfor
distributed communicating systems must address. Bigraphs are introduced first
informally,thenrigorously,beforebeingusedtodescribetheconfigurationofcom-
ponent agents. The static theory of Part I gives way in Part II to examining the
dynamicsofinteractions,leadingtothenotionofbehaviouralequivalenceandits
consequences.
The final Part explores a number of developments, in particular with regard
to ubiquitous computing and biological systems. Ideas for future research and
applicationsarepresented. Thebookisreasonablyself-containedmathematically,
andisdesignedtobelearnedfrom: examplesandexercisesabound,solutionsfor
thelatterareprovided.
Like Milner’s other work, this is destined to have far-reaching and profound
significance.

THE SPACE AND MOTION OF
COMMUNICATING AGENTS
ROBIN MILNER
UniversityofCambridge
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521490306
© Cambridge University Press 2009
This publication is in copyright. Subject to statutory exception and to the
provision of relevant collective licensing agreements, no reproduction of any part
may take place without the written permission of Cambridge University Press.
First published in print format 2009
ISBN-13 978-0-511-51679-5 eBook (EBL)
ISBN-13 978-0-521-49030-6 hardback
ISBN-13 978-0-521-73833-0 paperback
Cambridge University Press has no responsibility for the persistence or accuracy
of urls for external or third-party internet websites referred to in this publication,
and does not guarantee that any content on such websites is, or will remain,
accurate or appropriate.
toMyFamily:
Lucy,Barney,Chloë,
andinMemoryofGabriel

Contents
Prologue pageix
Acknowledgements xxi
PartI : Space 1
1 Theideaofbigraphs 3
2 Definingbigraphs 14
2.1 Bigraphsandtheirassembly 14
2.2 Mathematicalframework 18
2.3 Bigraphicalcategories 25
3 Algebraforbigraphs 28
3.1 Elementarybigraphsandnormalforms 28
3.2 Derivedoperations 33
4 Relativeandminimalbounds 39
5 Bigraphicalstructure 46
5.1 RPOsforbigraphs 46
5.2 IPOsinbigraphs 52
5.3 AbstractbigraphslackRPOs 57
6 Sorting 59
6.1 PlacesortingandCCS 59
6.2 Linksorting,arithmeticnetsandPetrinets 64
6.3 Theimpactofsorting 69
PartII : Motion 71
7 Reactionsandtransitions 73
7.1 Reactivesystems 74
7.2 Transitionsystems 77
7.3 Subtransitionsystems 84
vii
viii Contents
7.4 Abstracttransitionsystems 85
8 Bigraphicalreactivesystems 88
8.1 DynamicsforaBRS 89
8.2 DynamicsforaniceBRS 94
9 Behaviourinlinkgraphs 100
9.1 Arithmeticnets 100
9.2 Condition–eventnets 103
10 BehaviouraltheoryforCCS 110
10.1 SyntaxandreactionsforCCSinbigraphs 110
10.2 TransitionsforCCSinbigraphs 114
PartIII : Development 121
11 Furthertopics 123
11.1 Tracking 123
11.2 Growth 125
11.3 Binding 130
11.4 Stochastics 137
12 Background,developmentandrelatedwork 139
Appendices 146
AppendixA Technicaldetail 147
AppendixB Solutionstoexercises 162
Glossaryoftermsandsymbols 177
References 180
Index 185