Renaming and the weakest family of failure detectors

Yehuda Afek, Petr Kuznetsov, Israel Nir

Abstract: We address the question of the weakest failure detector to circumvent the impossibility of \((2n-2)\)-renaming in a system of up to \(n\) participating processes. We derive that in a restricted class of eventual failure detectors there does not exist a single weakest oracle, but a weakest family of oracles \(\zeta _n\): every two oracles in \(\zeta _n\) are incomparable, and every oracle that allows for solving renaming provides at least as much information about failures as one of the oracles in \(\zeta _n\). As a by product, we obtain one more evidence that renaming is strictly easier to solve than set agreement.