International audienceIn this paper, we propose to extend the condition-based approach introduced and developed by Most'efaoui et al. in 2001 by characterizing Vn f , the set of all the possible input vectors containing the values proposed by n processes. The condition-based approach consists in identifying sets of input vectors for which the consensus is directly solvable (i.e., in one communication step) in a pure asynchronous model despite up to f crashes. We focus on all the other input vectors. Among them, we identify those that allow to solve the consensus problem in two communication steps still in a pure asynchronous model. For the other ones, we rely on a distributed oracle that enables the input vectors to converge toward a good patterned vector with probability one. We specify a protocol that benefits from this approach to solve the consensus problem very simply and efficiently
