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Table of contents
Introduction [FR]
Contexte et Motivations
Contributions
Introduction [EN]
Context and Motivations
Contributions
1 Population Protocols
1.1 Population protocols and their computational power
1.1.1 Definitions
1.1.2 Computational power
1.2 Random Scheduler
1.3 Restricted Interactions
1.3.1 One-way interaction
1.3.2 Restricted communication graphs
1.4 Enhanced individual computational power
1.4.1 Unique identifiers
1.4.2 Passively mobile machines
1.5 Fault tolerance
1.5.1 Byzantine Agents
1.5.2 Crashes and Transient Failures
1.6 Self Stabilization
I Games and Population Protocols
2 Pavlovian Population Protocols
2.1 Elementary Game Theory
2.2 From Games To Population Protocols
2.3 Main Result
2.4 Threshold Predicates
2.5 Modulo Counting
2.6 Conclusion
3 Symmetric Games and protocols
3.1 Symmetric population protocols
3.2 Some simple exclusive Pavlovian protocols
3.2.1 Counting up to 3 exclusively
3.3 Some non-trivial Exclusive Pavlovian Protocols
3.3.1 Leader Election
3.3.2 Majority
3.3.3 Counting up to 2k
3.4 Conclusion
II Computing with Large Population Protocols
4 Large Population Protocols
4.1 An illustrative example
4.1.1 A General Theorem about Approximation of Diffusions
4.1.2 Proving convergence of our example
4.1.3 Giving a better Asymptotic Development of p(k)
4.2 General Framework
4.3 Computing with LPPs
4.4 Conclusion
5 The computational power of LPPs
5.1 Any computable number is algebraic
5.2 Computing Algebraic Numbers
5.2.1 Computing Rationals
5.2.2 Derandomization
5.2.3 Constructing Equilibria
5.2.4 Enforcing Stability
5.3 Conclusion
Conclusion and Perspectives
Conclusion
Perspectives
