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

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10 CHAPTER 2. THE LANGUAGE CCS ✬ ✫✉ ✩ coffee ✉ ✉ CS pub coin ✪ Figure 2.1: The interface for process CS all is the process 0 (read ‘nil’). This is the most boring process imaginable, as it performs no action whatsoever. The process 0 offers the prototypical example of a deadlocked behaviour—one that cannot proceed any further in its computation. The most basic process constructor in CCS is action prefixing. Two example processes built using 0 and action prefixing are a match and a complex match, described by the expressions strike.0 and take.strike.0 , respectively. Intuitively, a match is a process that dies when stricken (i.e., that becomes the process 0 after executing the action strike), and a complex match is one that needs to be taken before it can behave like a match. More in general, the formation rule for action prefixing says that: If P is a process and a is a label, then a.P is a process. The idea is that a label, like strike or pub, will denote an input or output action on a communication port, and that the process a.P is one that begins by performing action a and behaves like P thereafter. We have already mentioned that processes can be given names, very much like procedures can. This means that we can introduce names for (complex) processes, and that we can use these names in defining other process descriptions. For instance, we can give the name Match to the complex match thus: Match def = take.strike.0 . The introduction of names for processes allows us to give recursive definitions of process behaviours—compare with the recursive definition of procedures or methods in your favourite programming language. For instance, we may define the
2.1. SOME CCS PROCESS CONSTRUCTIONS 11 behaviour of an everlasting clock thus: Clock def = tick.Clock . Note that, since the process name Clock is a short-hand for the term on the righthand side of the above equation, we may repeatedly replace the name Clock with its definition to obtain that Clock def = tick.Clock = tick.tick.Clock = tick.tick.tick.Clock . = tick. . . . .tick .Clock , n-times for each positive integer n. As another recursive process specification, consider that of a simple coffee vending machine: CM def = coin.coffee.CM . (2.1) This is a machine that is willing to accept a coin as input, deliver coffee to its customer, and thereafter return to its initial state. Choice The CCS constructs that we have presented so far would not allow us to describe the behaviour of a vending machine that allows its paying customer to choose between tea and coffee, say. In order to allow for the description of processes whose behaviour may follow different patterns of interaction with their environment, CCS offers the choice operator, which is written ‘+’. For example, a vending machine offering either tea or coffee may be described thus: CTM def = coin.(coffee.CTM + tea.CTM) . (2.2) The idea here is that, after having received a coin as input, the process CTM is willing to deliver either coffee or tea, depending on its customer’s choice. In general, the formation rule for choice states that: If P and Q are processes, then so is P + Q. The process P +Q is one that has the initial capabilities of both P and Q. However, choosing to perform initially an action from P will pre-empt the further execution of actions from Q, and vice versa.
Page 1: Reactive Systems: Modelling, Specif
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 30 and 31: 12 CHAPTER 2. THE LANGUAGE CCS Exer
Page 32 and 33: 14 CHAPTER 2. THE LANGUAGE CCS ✬
Page 34 and 35: 16 CHAPTER 2. THE LANGUAGE CCS ✬
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
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Page 44 and 45: 26 CHAPTER 2. THE LANGUAGE CCS Defi
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Page 52 and 53: 34 CHAPTER 2. THE LANGUAGE CCS To b
Page 55 and 56: Chapter 3 Behavioural equivalences
Page 57 and 58: 3.1. CRITERIA FOR A GOOD BEHAVIOURA
Page 59 and 60: 3.2. TRACE EQUIVALENCE: A FIRST ATT
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
Page 69 and 70: 3.3. STRONG BISIMILARITY 51 The imp
Page 71 and 72: 3.3. STRONG BISIMILARITY 53 Conclud
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Page 75 and 76: 3.3. STRONG BISIMILARITY 57 Recall
Page 77 and 78: 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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