Failure detectors in loosely named systems

This paper explores the power of failure detectors in read write shared memory systems with n processes whose names are drawn from the set {1, ..., m}, m ≥ 2n - 1. We do so by making an additional assumption, name obliviousness, on top of the three failure detector assumptions introduced by Zieliński. We present name non-oblivious failure detectors that are strong enough to wait-free solve the Symmetry Breaking (SB) problem, but not enough to solve the (n-1)- Set Consensus problem. Furthermore a family of weakest such failure detectors is presented. On the other hand we show that any non trivial name oblivious failure detector can wait-free solve (n - 1)-Set Consensus, by introducing a simple extension to anti-Ω;, the Loose-anti-Ω failure detector, and proving that it is the weakest failure detector that conforms to the four assumptions above.