, of IS runs on the left and the set of all IS runs represented as a simplicial complex on the right

, Preliminaries 2.1 Examples of valid sets of IS outputs, Chapter

, 60 4.3 Integration of adversary families, active resilience and collection of set-consensus objects inside a representation of agreement function classes, Agreement Functions 4.1 Relations between agreement function properties, p.64

, First and second iteration of the 2-dimensionnal barycentric subdivision of s. . 68 5.2 Second iteration of the 2-dimensionnal standard chromatic subdivision of s, Combinatorial Topology 5.1, p.69

, 74 6.2 3-processes affine tasks R 1?T &S and R 2?T &S with their facets displayed in blue, Affine Tasks 6.1, p.79

, 3-processes system, of all 2-contention simplices in Chr 2 s and some detailed IS runs, vol.87

, Facets of R 1 and R 2 in blue on top of the edges, in black, of Chr 2 s, p.88

, Critical simplices are displayed in orange (with p 2 the top vertex, p 1 the bottom left vertex and p 3 the bottom right vertex)

, Simplices in black, orange and green are mapped to concurrency levels of 0, 1 and 2 respectively (with p 2 the top vertex, p 1 the bottom left vertex and p 3 the bottom right vertex)

, Some examples of affine tasks R A in blue (with p 2 the top vertex, p 1 the bottom left vertex and p 3 the bottom right vertex)

, A view of 8 registers and processes with couples of independantly covered registers by processes p 1, Stable Storage in Comparison-Based Models

, A possible covering of r 1 , r 2 , r 3 and r 5 induced by the couples of independantly covered registers from Figure 7.1

, Graph representation of processes {p 5

119 7.5 Extended confusion from Figure 7.3 by making p 5 indistinguishably cover r 4 or r 6 ,

, Covering registers outside of the covering with all but one of the confused processes

, Addition of an alternative covering of the same size and for the same processes

, Two possible extensions of confusion size, either with initial or alternative confusions

139 8.2 Second and third iterations of the affine task characterizing the 3-proces testand-set model, First and second iteration of the candidate affine task for the wake-up adversarial model with participation equal to {p 1, vol.1 ,

21 2.2 Simulation of the AS memory in the IIS model for p i, Preliminaries 2.1 Level-based immediate snapshot implementation for p ,

30 3.4 Commit-abort object: algorithm for process i, Distributed Simulations 3.1 Shared memory simulation for simulator ,

, Abortable memory simulation for simulator s i

37 3.7 Round-based simulation for simulator s i ,

45 3.10 Adaptive set-consensus for t-resilient systems (for process p i ), p.48 ,

, Agreement Functions Chapter

80 6.2 Solution to R k in the n-processes (k + 1)-active-resilient model for process p i . . 88 6.3 Resolution of R A in the ?-model for process p i ,

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