In this paper, we offer new proofs to two lower bound results in distributed computing: a minimum of J + 1 and J + 2 rounds for reaching consensus and uniform consensus respectively when at most J 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 (fa) needs to be proved separately. The techniques used in the proof offer new insights into the lower bound results in distributed computing.
In REF , a novel oracle argument is introduced to prove both lower bounds for synchronous consensus and uniform consensus.
A unified proof of minimum time complexity for reaching consensus and uniform consensus - an oracle-based approach
21st IEEE Symposium on Reliable Distributed Systems, 2002. Proceedings.
21st IEEE Symposium on Reliable Distributed Systems, 2002. Proceedings.
Computer Science