Hi!
"CheckpointedAsynchronously" was a hint to the system that the state objects could be persisted asynchronously, i.e., that the stateful function could process data concurrently to the persisting operation.
However, this path was never implemented, so the hint was never used.
Flink 1.2 has not yet added an equivalent interface, because the interface being there without actual support for asynchronous operator state ended up confusing users.
Stephan