A unified proof of minimum time complexity for reaching consensus and uniform consensus - an oracle-based approach

In this paper, we offer new proofs to two lower bound results in distributed computing: a minimum of f+1 and f+2 rounds for reaching consensus and uniform consensus respectively when at most f fail-stop faults can happen. Here the computation model is synchronous message passing. Both proofs are based on a novel oracle argument. These two induction proofs are unified in the following sense: the induction steps are the same and only the initial step (f=0) needs to be proved separately. The techniques used in the proof offer new insights into the lower bound results in distributed computing.