  We compare the solvability of the Consensus and Broadcast problems in
synchronous communication networks in which the delivery of messages is not
reliable. The failure model is the mobile omission faults model. During each
round, some messages can be lost and the set of possible simultaneous losses is
the same for each round. We investigate these problems for the first time for
arbitrary sets of possible failures. Previously, these sets were defined by
bounding the numbers of failures.
  In this setting, we present a new necessary condition for the solvability of
Consensus that unifies previous impossibility results in this area. This
condition is expressed using Broadcastability properties. As a very important
application, we show that when the sets of omissions that can occur are defined
by bounding the numbers of failures, counted in any way (locally, globally,
etc.), then the Consensus problem is actually equivalent to the Broadcast
problem.
