  This paper addresses the consensus problem in homonymous distributed systems
where processes are prone to crash failures and have no initial knowledge of
the system membership ("homonymous" means that several processes may have the
same identifier). New classes of failure detectors suited to these systems are
first defined. Among them, the classes H\Omega\ and H\Sigma\ are introduced
that are the homonymous counterparts of the classes \Omega\ and \Sigma,
respectively. (Recall that the pair <\Omega,\Sigma> defines the weakest failure
detector to solve consensus.) Then, the paper shows how H\Omega\ and H\Sigma\
can be implemented in homonymous systems without membership knowledge (under
different synchrony requirements). Finally, two algorithms are presented that
use these failure detectors to solve consensus in homonymous asynchronous
systems where there is no initial knowledge of the membership. One algorithm
solves consensus with <H\Omega,H\Sigma>, while the other uses only H\Omega, but
needs a majority of correct processes.
  Observe that the systems with unique identifiers and anonymous systems are
extreme cases of homonymous systems from which follows that all these results
also apply to these systems. Interestingly, the new failure detector class
H\Omega\ can be implemented with partial synchrony, while the analogous class
A\Omega\ defined for anonymous systems can not be implemented (even in
synchronous systems). Hence, the paper provides us with the first proof showing
that consensus can be solved in anonymous systems with only partial synchrony
(and a majority of correct processes).
