I think we could reduce "local completion" to just "completion" throughout the text. I don't think the adjective "local" is necessary and in some ways I find it confusing. We define precisely what "completion" means in a collective, and we also explicitly note that completion at a process does not indicate the status of other processes. Whenever we say "local completion", we really mean "completion" by our definition, so "local" is not necessary here. And by saying "local" completion, it sounds as a reader that there may be such a thing as "non-local" completion, but we don't define it. There is only one definition for collective completion. -Adam p 2, line 17 in "Collective operations can (but are not required to) complete locally as soon as the caller's participation in the collective communication is finished." "complete locally" --> "complete" p 2, line 20 in "The local completion of a collective operation indicates that the caller is free to access locations in the communication buffer." "The local completion" --> "The completion" p 49, line 48 & p 50, line 1 in "Once initiated, all associated send buffers should not be modified and all associated receive buffers should not be accessed until the collective operation completes locally." "until the collective operation completes locally." --> "until the collective operation completes." p 51, line 32 in "On intracommunicators, the operation completes locally after every process in the communicator called MPI_IBARRIER." "the operation completes locally" --> "the operation completes" and (to preserve verb tense) "after every process in the communicator called" --> "after every process in the communicator calls"