Table of contents
I |
Introduction |
| 1 | Introduction |
| 1.1 | Real-Time Systems |
| 1.2 | Algebras and Automata |
| 1.3 | Our Contribution |
| 1.4 | Outline of the Dissertation |
| 2 | Preliminaries |
| 2.1 | Transition Systems |
| 2.2 |  - A Common Language for Untimed Behaviours |
| 2.3 | An Equational Theory for |
II |
Timed Systems |
| 3 | Timed Transition Systems |
| 3.1 | The Model |
| 3.2 | Timed Bisimulation |
| 4 | Timed Automata |
| 4.1 | Clocks and Clock Constraints |
| 4.2 | The Model |
| 4.3 | Semantics for Timed Automata |
| 4.4 | Equivalences on Timed Automata |
| 5 |  - Algebra for Real-Time Systems |
| 5.1 | Syntax |
| 5.2 | Semantics in Terms of Timed Automata |
| 5.3 | Timed Automata up to alpha-conversion |
| 5.4 | Representability |
| 5.5 | Congruences |
| 5.6 | An Operational Semantics for the Basic Language |
| 5.7 | Summary |
| 5.8 | Related Work |
| 6 | Equational Theory for |
| 6.1 | Basic Axioms |
| 6.2 | Axioms for the Static Operators |
| 6.3 | Conservative Extension |
| 7 | Further Examples using |
| 7.1 | Derived Operations |
| 7.2 | A Railroad Crossing |
| 7.3 | Regular Processes and Finite Timed Automata |
| 7.4 | Concluding Remarks |
III |
Stochastic Systems |
| 8 | Probabilistic Transition Systems |
| 8.1 | The Model |
| 8.2 | Probabilistic bisimulation |
| 8.3 | Concluding Remarks |
| 9 | Stochastic Automata |
| 9.1 | Clocks as Random Variables |
| 9.2 | The Model |
| 9.3 | Semantics of Stochastic Automata |
| 9.4 | Equivalences on Stochastic Automata |
| 9.5 | Stochastic Automata and GSMPs |
| 9.6 | Concluding Remarks |
| 10 |  - Stochastic Process Algebra for Discrete Event Systems |
| 10.1 | Syntax |
| 10.2 | Semantics in Terms of Stochastic Automata |
| 10.3 | Stochastic Automata up to alpha-conversion |
| 10.4 | Representability |
| 10.5 | Congruences |
| 10.6 | Summary |
| 10.7 | Related Work |
| 11 | Equational Theory for |
| 11.1 | Basic Axioms for Structural Bisimulation |
| 11.2 | Axioms and Laws for Open p-Bisimulation |
| 11.3 | Axioms for the Static Operators |
| 11.4 | Conservative Extension |
| 12 | Analysis of Specifications |
| 12.1 | Runs and Schedulers |
| 12.2 | Discrete Event Simulation |
| 12.3 | Reachability Analysis |
| 12.4 | Simple Queueing Systems |
| 12.5 | A Multiprocessor Mainframe |
| 12.6 | Transient Analysis in a Root Contention Protocol |
| 12.7 | Related Work |
| 12.8 | Concluding Remarks |
| 13 | Concluding Remarks |
| 13.1 | Achievements |
| 13.2 | Future Research Directions |
IV |
Technicalities |
| A | Proofs from Chapter 4 |
| A.1 | Structural Bisimulation is Transitive |
| A.2 | Proof of Theorem 4.20 (structural bisimulation implies timed bisimulation) |
| B | Proofs from Chapter 5 |
| B.1 | Alternative Definitions |
| B.2 | Proofs of Theorems 5.16 and 5.17 (alpha-congruence preserves structural bisimulation) |
| B.3 | Proof of Theorem 5.24 (Correctness of the direct semantics) |
| B.4 | Proof of Theorems 5.25 and 5.22 (Congruence of timed bisimulation) |
| C | Proofs from Chapter 6 |
| C.1 | Proof of Theorem 6.6 (Existence of basic terms) |
| D | Some Concepts of Probability Theory |
| D.1 | Probability Spaces and Measurable Functions |
| D.2 | Borel Spaces and Probability Measures |
| D.3 | Random Variables |
| D.4 | Some distributions |
| E | Proofs from Chapter 9 |
| E.1 | Structural Bisimulation is Transitive |
| E.2 | Proof of Theorem 9.20 (structural bisimulation implies open p-bisimulation) |
| E.3 | Proof of Theorem 9.21 (open p-bisimulation implies closed p-bisimulation) |
| F | Proofs from Chapter 10 |
| F.1 | Proofs of Theorems 10.17 and 10.18 (α-congruence preserves structural bisimulation) |
| F.2 | Proof of Theorem 10.24 (Congruence of open p-bisimulation) |
| G | Proofs from Chapter 11 |
| G.1 | Proof of Proposition 11.4 (Axioms preserve definability) |
| G.2 | Proof of Theorem 11.6 (Existence of basic terms) |
| G.3 | Proof of Theorem 11.12 (Soundness of ax(^b)+O) |
| Bibliography | |
| Nomenclature | |
| Index | |
| Abstract | |
| Samenvatting |
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