The Space and Motion of Communicating Agents

The Space and Motion of Communicating Agents

by Robin Milner
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Cambridge University Press

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The Space and Motion of Communicating Agents

The world is increasingly populated with interactive agents distributed in space, real or abstract. These agents can be artificial, as in computing systems that manage and monitor traffic or health; or they can be natural, e.g. communicating humans, or biological cells. It is important to be able to model networks of agents in order to understand and optimise their behaviour. Robin Milner's purpose is to describe in this book just such a model, and he does so by presenting a unified and rigorous structural theory, based on bigraphs, for systems of interacting agents. This theory is a bridge between the existing theories of concurrent processes and the aspirations for ubiquitous systems, whose enormous size challenges our understanding.

The book begins with an assessment of the problems that a structural model for distributed communicating systems must address. Bigraphs are introduced first informally, then rigorously, before being used to describe the configuration of component agents. The static theory of Part I gives way in Part II to examining the dynamics of interactions, leading to the notion of behavioural equivalence and its consequences.

The final Part explores a number of developments, in particular with regard to ubiquitous computing and biological systems. Ideas for future research and applications are presented.

The book is reasonably self-contained mathematically, and is designed to be learned from: examples and exercises abound, solutions for the latter are provided.

Product Details

ISBN-13: 9780521490306
Publisher: Cambridge University Press
Publication date: 05/31/2009
Pages: 214
Product dimensions: 6.00(w) x 9.00(h) x 0.70(d)

Table of Contents

Prologue pageix

Acknowledgements xxi

Part I Space 1

1 The idea of bigraphs 3

2 Defining bigraphs 14

2.1 Bigraphs and their assembly 14

2.2 Mathematical framework 18

2.3 Bigraphical categories 25

3 Algebra for bigraphs 28

3.1 Elementary bigraphs and normal forms 28

3.2 Derived operations 33

4 Relative and minimal bounds 39

5 Bigraphical structure 46

5.1 RPOs for bigraphs 46

5.2 IPOs in bigraphs 52

5.3 Abstract bigraphs lack RPOs 57

6 Sorting 59

6.1 Place sorting and CCS 59

6.2 Link sorting, arithmetic nets and Petri nets 64

6.3 The impact of sorting 69

Part II Motion 71

7 Reactions and transitions 73

7.1 Reactive systems 74

7.2 Transition systems 77

7.3 Sub transition systems 84

7.4 Abstract transition systems 85

8 Bigraphical reactive systems 88

8.1 Dynamics for a BRS 89

8.2 Dynamics for a nice BRS 94

9 Behaviour in link graphs 100

9.1 Arithmetic nets 100

9.2 Condition-event nets 103

10 Behavioural theory for CCS 110

10.1 Syntax and reactions for CCS in bigraphs 110

10.2 Transitions for CCS in bigraphs 114

Part III Development 121

11 Further topics 123

11.1 Tracking 123

11.2 Growth 125

11.3 Binding 130

11.4 Stochastics 137

12 Background, development and related work 139

Appendices 146

Appendix A Technical detail 147

Appendix B Solutions to exercises 162

Glossary of terms and symbols 177

References 180

Index 185

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