@article {IOPORT.06003525,
    author       = {Gafni, Eli and Kuznetsov, Petr},
    title        = {On set consensus numbers.},
    year         = {2011},
    journal      = {Distributed Computing},
    volume       = {24},
    number       = {3-4},
    issn         = {0178-2770},
    pages        = {149-163},
    publisher    = {Springer-Verlag, Berlin},
    doi          = {10.1007/s00446-011-0142-8},
    abstract     = {Summary: It is conjectured that the only way a failure detector (FD) can help solving $n$-process tasks is by providing $k$-set consensus for some $k\in \{1,\ldots ,n\}$ among all the processes. It was recently shown by Zieli\'nski that any FD that allows for solving a given $n$-process task that is unsolvable read-write wait-free, also solves $(n - 1)$-set consensus. In this paper, we provide a generalization of Zieli\'nski's result. We show that any FD that solves a colorless task that cannot be solved read-write $k$-resiliently, also solves $k$-set consensus. More generally, we show that every colorless task $T$ can be characterized by its set consensus number: the largest $k\in \{1,\ldots ,n\}$ such that $T$ is solvable $(k - 1)$-resiliently. A task $T$ with set consensus number $k$ is, in the failure detector sense, equivalent to $k$-set consensus, i.e., an FD solves $T$ if and only if it solves $k$-set consensus. As a corollary, we determine the weakest FD for solving $k$-set consensus in every environment, i.e., for all assumptions on when and where failures might occur.},
    identifier   = {06003525},
}