Uniform consensus is harder than consensus

We compare the consensus and uniform consensus problems in synchronous systems. In contrast to consensus, uniform consensus is not solvable 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. In this failure model, we examine the number of rounds required to reach a decision in the consensus and uniform consensus algorithms. We show that if uniform agreement is required, one additional round is needed to decide, and so uniform consensus is also harder than consensus for crash failures. This is based on a new lower bound result for the synchronous model that we state for the uniform consensus problem. Finally, an algorithm is presented hat achieves this lower bound.