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

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12 CHAPTER 2. THE LANGUAGE CCS Exercise 2.1 Give a CCS process that describes a clock that ticks at least once, and that may stop ticking after each clock tick. Exercise 2.2 Give a CCS process that describes a coffee machine that may behave like that given by (2.1), but may also steal the money it receives and fail at any time. Exercise 2.3 A finite process graph T is a quadruple (Q, A, δ, q0), where • Q is a finite set of states, • A is a finite set of labels, • q0 ∈ Q is the start state and • δ : Q × A → 2 Q is the transition function. Using the operators introduced so far, give a CCS process that ‘describes T ’. Parallel composition It is well-known that a computer scientist working in a research university is a machine for turning coffee into publications. The behaviour of such an academic may be described by the CCS process CS def = pub.coin.coffee.CS . (2.3) As made explicit by the above description, a computer scientist is initially keen to produce a publication—possibly straight out of her doctoral dissertation—, but she needs coffee to produce her next publication. Coffee is only available through interaction with the departmental coffee machine CM. In order to describe systems consisting of two or more processes running in parallel, and possibly interacting with each other, CCS offers the parallel composition operation, which is written ‘|’. For example, the CCS expression CM | CS describes a system consisting of two processes—the coffee machine CM and the computer scientist CS—that run in parallel one with the other. These two processes may communicate via the communication ports they share and use in complementary fashion, namely coffee and coin. By complementary, we mean that one of the processes uses the port for input and the other for output. Potential communications are represented in Figure 2.2 by the solid lines linking complementary ports. The port pub is instead used by the computer scientist to communicate with her research environment, or, more prosaically, with other processes that may be present in her environment and that are willing to accept input along that port. One important thing to note is that the link between complementary ports in Figure 2.2 denotes that it is possible for the
2.1. SOME CCS PROCESS CONSTRUCTIONS 13 ✬ CM ✫✉ coin ✩ ✪ ✬ CS ✫✉ coin ✩ coffee ✉ ✉ ✉ pub coffee Figure 2.2: The interface for process CM | CS ✪ computer scientist and the coffee machine to communicate in the parallel composition CM | CS. However, we do not require that they must communicate with one another. Both the computer scientist and the coffee machine could use their complementary ports to communicate with other reactive systems in their environment. For example, another computer scientist CS ′ can use the coffee machine CM, and, in so doing, make sure that he can produce publications to beef up his curriculum vitae, and thus be a worthy competitor for CS in the next competition for a tenured position. (See Figure 2.3.) Alternatively, the computer scientist may have access to another coffee machine in her environment, as pictured in Figure 2.4. In general, given two CCS expressions P and Q, the process P | Q describes a system in which • P and Q may proceed independently or • may communicate via complementary ports. Restriction and relabelling Since academics like the computer scientist often live in a highly competitive ‘publish or perish’ environment, it may be fruitful for her to make the coffee machine CM private to her, and therefore inaccessible to her competitors. To make this possible, the language CCS offers an operation called restriction, whose aim is to delimit the scope of channel names in much the same way as variables have scope in block structured programming languages. For instance, using the operations \coin and \coffee, we may hide the coin and coffee ports from the environment of the processes CM and CS. Define the process SmUni (for ‘Small University’) thus: SmUni def = (CM | CS) \ coin \ coffee . (2.4)
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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 42 and 43: 24 CHAPTER 2. THE LANGUAGE CCS •
Page 44 and 45: 26 CHAPTER 2. THE LANGUAGE CCS Defi
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Page 55 and 56: Chapter 3 Behavioural equivalences
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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
Page 73 and 74: 3.3. STRONG BISIMILARITY 55 3. the
Page 75 and 76: 3.3. STRONG BISIMILARITY 57 Recall
Page 77 and 78: 3.3. STRONG BISIMILARITY 59 B 2 0
Page 79 and 80: 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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