Reactive Systems: Modelling, Specification and Verification - Cs.ioc.ee

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iv CONTENTS 5 Hennessy-Milner logic 101 6 Hennessy-Milner logic with recursive definitions 115 6.1 Examples of recursive properties . . . . . . . . . . . . . . . . . . 120 6.2 Syntax and semantics of HML with recursion . . . . . . . . . . . 122 6.3 Largest fixed points and invariant properties . . . . . . . . . . . . 127 6.4 A game characterization for HML with recursion . . . . . . . . . 128 6.4.1 Examples of use . . . . . . . . . . . . . . . . . . . . . . 131 6.5 Mutually recursive equational systems . . . . . . . . . . . . . . . 134 6.6 Characteristic properties . . . . . . . . . . . . . . . . . . . . . . 139 6.7 Mixing largest and least fixed points . . . . . . . . . . . . . . . . 149 6.8 Further results on model checking . . . . . . . . . . . . . . . . . 154 7 Modelling and analysis of mutual exclusion algorithms 157 7.1 Specifying mutual exclusion in HML . . . . . . . . . . . . . . . . 162 7.2 Specifying mutual exclusion using CCS itself . . . . . . . . . . . 164 7.3 Testing mutual exclusion . . . . . . . . . . . . . . . . . . . . . . 168 II A theory of real-time systems 175 8 Introduction 177 9 CCS with time delays 179 9.1 Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 9.2 Timed labelled transition systems . . . . . . . . . . . . . . . . . . 181 9.3 Syntax and SOS rules of timed CCS . . . . . . . . . . . . . . . . 184 9.4 Parallel composition . . . . . . . . . . . . . . . . . . . . . . . . 187 9.5 Other timed process algebras and discussion . . . . . . . . . . . . 191 10 Timed automata 195 10.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 10.2 Syntax of timed automata . . . . . . . . . . . . . . . . . . . . . . 196 10.3 Semantics of timed automata . . . . . . . . . . . . . . . . . . . . 200 10.4 Networks of timed automata . . . . . . . . . . . . . . . . . . . . 206 10.5 Further on timed automata formalisms . . . . . . . . . . . . . . . 211 11 Timed behavioural equivalences 215 11.1 Timed and untimed trace equivalence . . . . . . . . . . . . . . . 215 11.2 Timed and untimed bisimilarity . . . . . . . . . . . . . . . . . . . 217 11.3 Weak timed bisimilarity . . . . . . . . . . . . . . . . . . . . . . . 223
CONTENTS v 11.4 Region graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 11.5 Zones and reachability graph . . . . . . . . . . . . . . . . . . . . 237 11.6 Further results on timed equivalences . . . . . . . . . . . . . . . . 241 12 Hennessy-Milner logic with time 243 12.1 Basic logic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 12.2 Hennessy-Milner logic with time and regions . . . . . . . . . . . 253 12.3 Timed bisimilarity vs HML with time . . . . . . . . . . . . . . . 256 12.4 Recursion in HML with time . . . . . . . . . . . . . . . . . . . . 261 12.5 More on timed logics . . . . . . . . . . . . . . . . . . . . . . . . 271 13 Modelling and analysis of Fischer’s algorithm 273 13.1 Mutual exclusion using timing . . . . . . . . . . . . . . . . . . . 275 13.2 Modelling Fischer’s algorithm . . . . . . . . . . . . . . . . . . . 276 13.2.1 Proving mutual exclusion using UPPAAL . . . . . . . . . 278 13.2.2 An erroneous version of Fischer’s algorithm . . . . . . . . 281 13.3 Further exercises on timing based mutual exclusion algorithms . . 282 A Suggestions for student projects 287 A.1 Alternating bit protocol . . . . . . . . . . . . . . . . . . . . . . . 287 A.2 Gossiping girls . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 A.3 Implementation of regions . . . . . . . . . . . . . . . . . . . . . 289 Bibliography 293 Index 310
Page 1: Reactive Systems: Modelling, Specif
Page 7 and 8: List of Figures 2.1 The interface f
Page 9: List of Tables 2.1 An alternative f
Page 12 and 13: xii PREFACE It has been very satisf
Page 14 and 15: xiv PREFACE a textbook, and offers
Page 16 and 17: xvi PREFACE studies in Edinburgh, a
Page 19: Part I A classic theory of reactive
Page 22 and 23: 4 CHAPTER 1. INTRODUCTION After hav
Page 24 and 25: 6 CHAPTER 1. INTRODUCTION • softw
Page 26 and 27: 8 CHAPTER 1. INTRODUCTION prototype
Page 28 and 29: 10 CHAPTER 2. THE LANGUAGE CCS ✬
Page 30 and 31: 12 CHAPTER 2. THE LANGUAGE CCS Exer
Page 36 and 37: 18 CHAPTER 2. THE LANGUAGE CCS CS d
Page 38 and 39: 20 CHAPTER 2. THE LANGUAGE CCS Sinc
Page 40 and 41: 22 CHAPTER 2. THE LANGUAGE CCS a p
Page 42 and 43: 24 CHAPTER 2. THE LANGUAGE CCS •
Page 44 and 45: 26 CHAPTER 2. THE LANGUAGE CCS Defi
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Chapter 3 Behavioural equivalences
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3.1. CRITERIA FOR A GOOD BEHAVIOURA
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3.2. TRACE EQUIVALENCE: A FIRST ATT
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3.3. STRONG BISIMILARITY 43 trace e
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3.3. STRONG BISIMILARITY 45 Obvious
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3.3. STRONG BISIMILARITY 47 So, by
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3.3. STRONG BISIMILARITY 49 Theorem
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3.3. STRONG BISIMILARITY 51 The imp
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3.3. STRONG BISIMILARITY 53 Conclud
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3.3. STRONG BISIMILARITY 55 3. the
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3.3. STRONG BISIMILARITY 57 Recall
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3.3. STRONG BISIMILARITY 59 B 2 0
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3.4. WEAK BISIMILARITY 61 Is there
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3.4. WEAK BISIMILARITY 63 Start pu
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3.4. WEAK BISIMILARITY 65 Our order
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3.4. WEAK BISIMILARITY 67 Send def
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3.4. WEAK BISIMILARITY 69 Show that
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3.4. WEAK BISIMILARITY 71 In light
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3.5. GAME CHARACTERIZATION OF BISIM
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CHAPTER 3.5. GAME CHARACTERIZATION
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3.6. FURTHER RESULTS ON EQUIVALENCE
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3.6. FURTHER RESULTS ON EQUIVALENCE
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86 CHAPTER 4. THEORY OF FIXED POINT
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Chapter 5 Hennessy-Milner logic In
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103 We are interested in using the
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105 of the one step transitions a
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1. Decide whether the following sta
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109 Note that logical negation is n
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111 Another example of a process th
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a s s1 b s2 b a a t b t1 b t
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Chapter 6 Hennessy-Milner logic wit
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CHAPTER 6. HML WITH RECURSION 117 e
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CHAPTER 6. HML WITH RECURSION 119
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6.1. EXAMPLES OF RECURSIVE PROPERTI
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6.2. SYNTAX AND SEMANTICS OF HML WI
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6.2. SYNTAX AND SEMANTICS OF HML WI
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6.3. LARGEST FIXED POINTS AND INVAR
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6.4. GAME CHARACTERIZATION FOR HML
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6.5. MUTUALLY RECURSIVE EQUATIONAL
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6.5. MUTUALLY RECURSIVE EQUATIONAL
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6.6. CHARACTERISTIC PROPERTIES 139
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6.7. MIXING LARGEST AND LEAST FIXED
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6.8. FURTHER RESULTS ON MODEL CHECK
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Chapter 7 Modelling and analysis of
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CHAPTER 7. MODELLING MUTUAL EXCLUSI
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CHAPTER 7. MODELLING MUTUAL EXCLUSI
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7.1. SPECIFYING MUTUAL EXCLUSION IN
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7.2. SPECIFYING MUTUAL EXCLUSION US
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7.2. SPECIFYING MUTUAL EXCLUSION US
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7.3. TESTING MUTUAL EXCLUSION 169 i
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7.3. TESTING MUTUAL EXCLUSION 171 D
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7.3. TESTING MUTUAL EXCLUSION 173 1
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Reactive Systems: Modelling, Specification and Verification - Cs.ioc.ee

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