Consensus with Max Registers.

We consider the problem of implementing randomized wait-free consensus from max registers under the assumption of an oblivious adversary. We show that max registers solvem-valued consensus for arbitrarym in expectedO(log∗ n) steps per process, beating the Ω ( log m log log m ) lower bound for ordinary registers when m is large and the best previously known O(log logn) upper bound when m is small. A simple max-register implementation based on double-collect snapshots translates this result into an O(n logn) expected step implementation of m-valued consensus from n single-writer registers, improving on the best previously-known bound of O(n log2 n).