springer concurrency theory 7 potx

[...]... 213 7 Comparison of LOTOS with CCS and CSP 215 7. 1 CCS and LOTOS 2 17 7.1.1 Parallel Composition and Complementation of Actions 2 17 7.1.2 Restriction and Hiding 220 7. 1.3 Internal Behaviour 221 7. 1.4 Minor Differences 221 7. 2 CSP and LOTOS... 222 7. 2.1 Alphabets 222 7. 2.2 Internal Actions 224 7. 2.3 Choice 225 7. 2.4 Parallelism 2 27 7.2.5 Hiding 2 27 XXII Contents 7. 2.6 Comparison of LOTOS Trace-refusals with... 270 9.2.4 Nondeterminism 271 9.2.5 Synchronisation 272 9.2.6 Timing Domains 273 9.2 .7 Time Measurement 273 9.2.8 Timing of Nonadjacent Actions 274 9.2.9 Timed Interaction Policies 275 9.2.10 Forms of Internal... clarified what we mean by concurrency theory However, this leaves the question of what we mean by a mathematical theory of concurrency In a broad sense, our mathematical theory of concurrency has the same ingredients as the familiar mainstream mathematical theories, such as, for example, the theory of (counting) numbers (which is the heart of the mathematical discipline of number theory) We illustrate... important relation is equality For example, in the theory of numbers, (X + 73 ) × 3 = ((X + 72 ) × 3) + 3 The fact that these 12 1 Background on Concurrency Theory two expressions are equal is justified by the fact that whatever value you plug in for X, the two expressions evaluate to the same value In a similar way to equality in the theory of numbers, the theory of concurrency defines notions of equality, but... We illustrate this by comparing the ingredients of the theory of numbers with those of concurrency theory 1 Values These are the primitive elements in mathematical theories They are the basic objects that the theory is about The values in the theory of numbers are the integers, , –3, –2, –1, 0, 1, 2, 3, In contrast, values in concurrency theory denote the behaviour of concurrent systems The event... 368 12.5 Timelock Detection in Real-time Model-checkers 374 12.5.1 Uppaal 374 12.5.2 Kronos 376 13 Discrete Timed Automata 377 13.1 Infinite vs Finite States 377 13.2 Preliminaries 380 13.2.1... Part II Concurrency Theory – Untimed Models 17 This part contains core concurrency theory material We present the process calculus pbLOTOS from first principles in Chapter 2, illustrating the approach with a number of running examples Then, in Chapters 3, 4 and 5, we consider how this calculus can be interpreted semantically In particular, we motivate the use of semantic models in concurrency theory. .. used in the theory of numbers to express how numbers can be transformed into other numbers In concurrency theory we also have operators, e.g ||| and [] The former of these 1.4 Mathematical Theories 4 5 6 7 11 denotes a particular form of parallel composition and the second a choice between two alternatives Expressions Arithmetical expressions can be defined in the theory of numbers, e.g (X + 73 ) × 3 These... Trace-refusals Relations in Distributed Systems 166 5.4.1 Relating OO Concepts to LOTOS 166 5.4.2 Behavioural Subtyping 1 67 5.4.3 Viewpoints and Consistency 177 Part III Concurrency Theory – Further Untimed Notations 6 Beyond pbLOTOS 185 6.1 Basic LOTOS 185 . 221 7. 1.4 MinorDifferences 221 7. 2 CSPandLOTOS 222 7. 2.1 Alphabets 222 7. 2.2 Internal Actions 224 7. 2.3 Choice 225 7. 2.4 Parallelism 2 27 7.2.5 Hiding 2 27 XXII Contents 7. 2.6 Comparison of LOTOS Trace-refusals. 213 7 Comparison of LOTOS with CCS and CSP 215 7. 1 CCS andLOTOS 2 17 7.1.1 Parallel Composition and Complementation of Actions . 2 17 7.1.2 RestrictionandHiding 220 7. 1.3 Internal Behaviour 221 7. 1.4. Persistency 270 9.2.4 Nondeterminism 271 9.2.5 Synchronisation 272 9.2.6 TimingDomains 273 9.2 .7 TimeMeasurement 273 9.2.8 TimingofNonadjacentActions 274 9.2.9 TimedInteractionPolicies 275 9.2.10