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The Reliable Broadcast concept allows an honest party to send a message toall other parties and to make sure that all honest parties receive thismessage. In addition, it allows an honest party that received a message to knowthat all other honest parties would also receive the same message. Thistechnique is important to ensure distributed consistency when facing failures.  In the current paper, we study the ability to use \RR to consistentlytransmit a sequence of input values in an asynchronous environment with adesignated sender. The task can be easily achieved using counters, but cannotbe achieved with a bounded memory facing failures. We weaken the problem andask whether the receivers can at least share a common suffix. We prove that ina standard (lossless) asynchronous system no bounded memory protocol canguarantee a common suffix at all receivers for every input sequence if a singleparty might crash.  We further study the problem facing transient faults and prove that whenlimiting the problem to transmitting a stream of a single value being sentrepeatedly we show a bounded memory self-stabilizing protocol that can ensure acommon suffix even in the presence of transient faults and an arbitrary numberof crash faults. We further prove that this last problem is not solvable in thepresence of a single Byzantine fault. Thus, this problem {\bf separates}Byzantine behavior from crash faults in an asynchronous environment.

Possibility and Impossibility of Reliable Broadcast in the Bounded Model