[...]... 13 4 4.8 Summary and Discussion 13 8 5 Testing Theory and the Linear Time – Branching Time Spectrum 14 1 5 .1 Trace-refusals Semantics 14 1 5 .1. 1 Introduction 14 1 5 .1. 2 The Basic Approach 14 3 5 .1. 3 Deriving Trace-refusal... 3 21 11. 2 Timed Automata – Formal Definitions 323 11 .2 .1 Syntax 324 11 .2.2 Semantics 325 11 .3 Real-time Model-checking 332 11 .3 .1 Forward Reachability 333 11 .3.2 Example: Reachability Analysis on the... 10 Semantic Models for tLOTOS 287 10 .1 Branching Time Semantics 287 10 .1. 1 Timed Transition Systems 287 10 .1. 2 Operational Semantics 289 10 .1. 3 Branching Time Development Relations 299 10 .2 True Concurrency Semantics 304 Contents XXIII 10 .2 .1. .. 14 5 5 .1. 4 Internal Behaviour 14 6 5 .1. 5 Development Relations: Equivalences 15 2 5 .1. 6 Nonequivalence Development Relations 15 4 5 .1. 7 Explorations of Congruence 15 8 5 .1. 8 Summary and Discussion 15 9 5.2 Testing Justification for Trace-refusals Semantics 16 0 5.3 Testing Theory. .. 3 41 11. 3.3 Issues in Real-time Model-checking 342 12 Timelocks in Timed Automata 347 12 .1 Introduction 347 12 .2 A Classification of Deadlocks in Timed Automata 349 12 .2 .1 Discussion: Justifying the Classification of Deadlocks 350 12 .2.2 Discussion: Timelocks in Process Calculi 3 51 12.3... 3 61 12.4.3 Nonzenoness: A Sufficient-and-Necessary Condition 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... 16 1 5.3 .1 Sequence-based Testing 16 2 5.3.2 Tree-based Testing 16 3 Contents XXI 5.4 Applications of Trace-refusals Relations in Distributed Systems 16 6 5.4 .1 Relating OO Concepts to LOTOS 16 6 5.4.2 Behavioural Subtyping 16 7 5.4.3 Viewpoints and Consistency 17 7 Part... 17 7 Part III Concurrency Theory – Further Untimed Notations 6 Beyond pbLOTOS 18 5 6 .1 Basic LOTOS 18 5 6 .1. 1 Disabling 18 5 6 .1. 2 Generalised Choice 18 8 6 .1. 3 Generalised Parallelism 18 9 6 .1. 4 Verbose Specification... Part I Introduction 1 Background on Concurrency Theory 3 1. 1 Concurrency Is Everywhere 3 1. 2 Characteristics of Concurrent Systems 4 1. 3 Classes of Concurrent Systems 6 1. 3 .1 Basic Event Ordering 6 1. 3.2 Timing Axis 7 1. 3.3 Probabilistic... Preliminaries 380 13 .2 .1 Fair Transition Systems and Invariance Proofs 3 81 13.2.2 The Weak Monadic Second-order Theory of 1 Successor (WS1S) and MONA 383 13 .3 Discrete Timed Automata – Formal definitions 384 13 .3 .1 Syntax 384 13 .3.2 Example: A DTA Specification for the Multimedia . Library Library of Congress Control Number: 20059 314 33 ISBN -1 0 : 1- 8 523 3-8 9 5-4 ISBN -1 3 : 97 8 -1 -8 523 3-8 9 5-4 Printed on acid-free paper © Springer- Verlag London Limited 2006 Apart from any fair dealing. Trace-refusalsSemantics 14 1 5 .1. 1 Introduction 14 1 5 .1. 2 TheBasicApproach 14 3 5 .1. 3 Deriving Trace-refusal Pairs 14 5 5 .1. 4 Internal Behaviour 14 6 5 .1. 5 DevelopmentRelations: Equivalences 15 2 5 .1. 6 Nonequivalence. Subtyping 16 7 5.4.3 ViewpointsandConsistency 17 7 Part III Concurrency Theory – Further Untimed Notations 6 Beyond pbLOTOS 18 5 6 .1 Basic LOTOS 18 5 6 .1. 1 Disabling 18 5 6 .1. 2 GeneralisedChoice 18 8 6 .1. 3