Looking for the optimal conditions for solving set agreement

The set agreement power of a shared object O describes O's ability to solve set agreement problems: it is the sequence (n_1, n_2, ..., n_k, ...) such that, for every k >= 1, using O and registers one can solve the k-set agreement problem among at most n_...

The set agreement power of a shared object O describes O’s ability to solve set agreement problems: it is the sequence $(n_1,n_2,\dots ,n_k,\dots )$ such that, for every $k\ge 1$, using O and registers one can solve the k-set agreement problem among at most $n_k$ ...$\mathrm{}$$\mathrm{}$${}_{}$${}_{\mathrm{}}{}_{\mathrm{}}{}_{}$${}_{}$$\mathrm{}$${}_{}$

In the traditional consensus task, processes are required to agree on a common value chosen among the initial values of the participating processes. It is well known that consensus cannot be solved in crash-prone, asynchronous distributed systems. Two ...