Exact Fault-Tolerant Consensus with Voting Validity

This paper investigates the multi-valued fault-tolerant distributed consensus problem that pursues exact output. To this end, the voting validity, which requires the consensus output of non-faulty nodes to be the exact plurality of the input of non-faulty nodes, is investigated. Considering a specific distribution of nonfaulty votes, we first give the impossibility results and a tight lower bound of system tolerance achieving agreement, termination and voting validity. A practical consensus algorithm that satisfies voting validity in the Byzantine fault model is proposed subsequently. To ensure the exactness of outputs in any non-faulty vote distribution, we further propose safety-critical tolerance and a corresponding protocol that prioritizes voting validity over termination property. To refine the proposed protocols, we propose an incremental threshold algorithm that accelerates protocol operation speed. We also optimize consensus algorithms with the local broadcast model to enhance the protocol's fault tolerance ability.