  The Heard-Of model is a simple and relatively expressive model of distributed
computation. Because of this, it has gained a considerable attention of the
verification community. We give a characterization of all algorithms solving
consensus in a fragment of this model. The fragment is big enough to cover many
prominent consensus algorithms. The characterization is purely syntactic: it is
expressed in terms of some conditions on the text of the algorithm. One of the
recent methods of verification of distributed algorithms is to abstract an
algorithm to the Heard-Of model and then to verify the abstract algorithm using
semi-automatic procedures. Our results allow, in some cases, to avoid the
second step in this methodology.
