A global checkpoint is a set of local checkpoints, one per process. The tra
ditional consistency criterion for global checkpoints states that a global
checkpoint is consistent if it does not include messages received and not s
ent. This paper investigates other consistency criteria, transitlessness, a
nd strong consistency. A global checkpoint is transitless if it does not ex
hibit messages sent and nor received. Transitlessness can be seen as a dual
of traditional consistency. Strong consistency is the addition of transitl
essness to traditional consistency. The main result of this paper is a stat
ement of the necessary and sufficient condition answering the following que
stion: "Given an arbitrary set of local checkpoints, can this set be extend
ed to a global checkpoint that satisfies P-m (where LP is traditional consi
stency, transitlessness, or strong consistency). From a practical point of
view, this condition, when applied to transitlessness, is particularly inte
resting as it helps characterize which messages do not need to be recorded
by checkpointing protocols.