is the minimum of two quantities:
: A lower bound on the send timestamp of the
next message P would send if it did not get additional messages or
acknowledgements.
: A lower bound on the send timestamp of the
next acknowledgement P would send if it did not get additional messages or
acknowledgments.
depends on the execution status of P:
is 
is
.
is calculated
by computing
the potential match of the unsafe messages in P's message
queues (i.e. on each communicator
C, messages that have a timestamp greater than or equal to
) with P's request list. Let the receive timestamp
of the message that potentially matches the request on which P is
blocked be 
(which is 
if there is no match).
Consequently, 
is the time at which P
would potentially resume execution. It might immediately send a message.
Consequently, 
is 
.
is also calculated by computing
the potential match of the unsafe
messages in P's message queues with P's request list.
Let 
be the earliest send timestamp of the acknowledgements
that are potentially sent on communicator C due to
this matching (which is 
if
there is no potential match on communicator C).
is 
i.e. the earliest acknowledgement on all communicators of which
P is a member.
Notice that if an LP P is in deterministic mode, there are
no unsafe messages. Consequently, both 
and
can be set to 
.