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Table of contents
1. Introduction en français
1.1. Synthèse de programmes
1.2. Les systèmes réactifs
1.3. La synthèse réactive et le problème de Church
1.4. Extension aux alphabets infinis
1.5. Extension au cas asynchrone
1.6. Plan
1.7. Comment lire cette thèse ?
2. Introduction in English
2.1. Program Synthesis
2.2. Reactive Systems
2.3. Reactive Synthesis and the Church Problem
2.4. Extension to the Infinite Alphabet Case
2.5. Further Extension to the Asynchronous Case
2.6. Outline
2.7. How to Read this Thesis?
I. Reactive Synthesis
3. Reactive Synthesis over Finite Alphabets
3.1. Relations and Functions
3.2. Uniformisation and Program Synthesis
3.3. The Reactive Synthesis Problem
3.4. The Church Synthesis Problem
3.5. Games for Reactive Synthesis
4. Register Automata over a Data Domain
4.1. DataWords
4.2. Tests and Valuations
4.3. Register Automata
4.4. General Properties
4.5. Non-Deterministic Register Automata with Equality
4.6. Non-Deterministic Register Automata with a Dense Order
4.7. Register Automata with a Discrete Order
4.8. Universal Register Automata
4.9. Register Automata and Arithmetic
4.10. Extensions of the Model
5. Synthesis Problems over DataWords
5.1. Reactive Synthesis over DataWords
5.2. Data Automatic Specifications
5.3. Register Transducers
5.4. The Church Synthesis Problem
6. Register-Bounded Synthesis of Register Transducers
6.1. A Generic Approach
6.2. Universal Register Automata Specifications
6.3. Non-Deterministic Register Automata Specifications
7. Unbounded Synthesis of Register Transducers
7.1. Non-Deterministic Register Automata Specifications
7.2. Universal Register Automata Specifications
7.3. Deterministic Register Automata Specifications
8. Partial Versus Total Domain
8.1. Domains of Specification Automata
8.2. Uniformisation Problem
8.3. Good-Enough Synthesis
9. Conclusion
II. Computability of Functions Defined by Transducers over Infinite Alphabets
10. Non-Deterministic Asynchronous Register Transducers
10.1. The Model
10.2. Register Transducers and Register Automata
10.3. Functions Recognised by Transducers
10.4. Closure under Composition
11. $-Computability and Continuity
11.1. Computability
11.2. Continuity
11.3. $-Computability versus Continuity
12. Exploration of Various Data Domains
12.1. Data Domains with Equality
12.2. Oligomorphic Data Domains
12.3. Discretely Ordered Data Domains
13. Conclusion
14. Thesis Conclusion
14.1. Abstraction of the Behaviour of Register Automata
14.2. Generalisation to Other Formalisms
14.3. Minimisation and Learning
