Let CSMPn,t[GO] be the system model CSMPn,t[∅] weakened as follows: a faulty process is
a process that crashes, or a process that forgets to send or receive messages. This is the general
omission failure model.
• Show that the model constraint t <>
system model CSMPn,t[GO]. (Hint: partition the set of processes in two subsets Q1 and
Q2 of size [n/2 ], and[n/2 ], and consider the case where, while no process crashes, all the
processes of Q2 commit send and receive omission failures with respect to the processes
of Q1.)
Remark. The proof is based on an indistinguishability argument as already used in the
proofs of some theorems (e.g., Theorem 9 and Theorem 18).
Solution in Chapter 7 of [367].
• Design and proof a consensus algorithm for the system model CSMPn,t[GO]. As a faulty
process may not crash, and may remain isolated from the correct processes, it cannot
decide the value decided by the correct processes. In this case, it is allowed to decide a
special default value denoted ⊥. Hence, if a process, that does not crash, decides ⊥, it
knows that it is faulty.
Let us remark that the existence of such an algorithm, shows that the model constraint
t <>
Solution in Chapter 7 of [356].