We study the time complexity of different agreement problems in the synchrono- us model with crash failures, by varying their validity condition. We first introduce a continuous class of agreement problems, the k-TAg problems, which includes both the Uniform Consensus and Non-Blocking Atomic Commitment. We then exhibit a general early-deciding algorithm, that we instanciate to solve every problem of this class. The algorithm always achieves the previously established lower-bounds for early-deciding, showing that these lower-bounds are tight.
