Uniform Consensus Harder than Consensus

We compare the consensus problem with the uniform consensus problem in synchronous systems. In contrast to consensus, uniform consensus is not solvable in synchronous systems with byzantine failures. This still holds for the omission failure model if a majority of processes may be faulty. For the crash failure model, both consensus and uniform consensus are solvable, no matter how many processes are faulty. We consider this failure model and we examine the number of rounds required to reach a decision in consensus and uniform consensus algorithms. We show that compared with the best consensus algorithm, any uniform consensus algorithm takes at least one additional round to take a decision. We thus prove that uniform consensus is also harder than consensus whatever the failure model is.