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

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18 CHAPTER 2. THE LANGUAGE CCS CS def = pub.CS1 CS1 CS2 def = coin.CS2 def = coffee.CS Table 2.1: An alternative formulation for process CS instance, for the purpose of notational convenience in what follows, let us redefine the process CS (originally defined in equation 2.3 on page 12) as in Table 2.1. (This is the definition of the process CS that we shall use from now on, both when discussing its behaviour in isolation and in the context of other processes—for instance, as a component of the process SmUni.) Process CS can perform action pub and evolve into a process whose behaviour is described by the CCS expression CS1 in doing so. Process CS1 can then output a coin, thereby evolving into a process whose behaviour is described by the CCS expression CS2. Finally, this process can receive coffee as input, and behave like our good old CS all over again. Thus the processes CS, CS1 and CS2 are the only possible states of the computation of process CS. Note, furthermore, that there is really no conceptual difference between processes and their states! By performing an action, a process evolves to another process that describes what remains to be executed of the original one. In CCS, processes change state by performing transitions, and these transitions are labelled by the action that caused them. An example state transition is CS pub → CS1 , which says that CS can perform action pub, and become CS1 in doing so. The operational behaviour of our computer scientist CS is therefore completely described by the following labelled transition system. coffee CS pub CS1 coin CS2 In much the same way, we can make explicit the set of states of the coffee machine described in equation 2.1 on page 11 by rewriting that equation thus: CM def = coin.CM1 CM1 def = coffee.CM .
2.1. SOME CCS PROCESS CONSTRUCTIONS 19 Note that the computer scientist is willing to output a coin in state CS1, as witnessed by the transition CS1 coin → CS2 , and the coffee machine is willing to accept that coin in its initial state, because of the transition CM coin → CM1 . Therefore, when put in parallel with one another, these two processes may communicate and change state simultaneously. The result of the communication should be described as a state transition of the form CM | CS1 ? → CM1 | CS2 . However, we are now faced with an important design decision—namely, we should decide what label to use in place of the ‘?’ labelling the above transition. Should we decide to use a standard label denoting input or output on some port, then a third process might be able to synchronize further with the coffee machine and the computer scientist, leading to multi-way synchronization. The choice made by Milner in his design of CCS is different. In CCS, communication is via handshake, and leads to a state transition that is unobservable, in the sense that it cannot synchronize further. This state transition is labelled by a new label τ. So the above transition is indicated by CM | CS1 τ → CM1 | CS2 . In this way, the behaviour of the process SmUni defined by equation 2.4 on page 13 can be described by the following labelled transition system. SmUni pub (CM | CS1) \ coin \ coffee (CM1 | CS2) \ coin \ coffee (CM | CS) \ coin \ coffee τ τ pub
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Page 4 and 5: iv CONTENTS 5 Hennessy-Milner logic
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 ✬
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Page 38 and 39: 20 CHAPTER 2. THE LANGUAGE CCS Sinc
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Page 61 and 62: 3.3. STRONG BISIMILARITY 43 trace e
Page 63 and 64: 3.3. STRONG BISIMILARITY 45 Obvious
Page 65 and 66: 3.3. STRONG BISIMILARITY 47 So, by
Page 67 and 68: 3.3. STRONG BISIMILARITY 49 Theorem
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Page 75 and 76: 3.3. STRONG BISIMILARITY 57 Recall
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Page 79 and 80: 3.4. WEAK BISIMILARITY 61 Is there
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Page 83 and 84: 3.4. WEAK BISIMILARITY 65 Our order
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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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