Design and Verification of Adaptive Cache Coherence Protocols ...

Notations Given a system term s, we use Mem(s), Min(s) and Mout(s) to represent the
memory, the memory's incoming queue and the memory's outgoing queue, respectively. For
a cache site id , we use Cacheid (s), Cinid(s), Coutid(s), Pmbid(s), Mpbid(s) and Procid(s) to
represent the cache, the incoming queue, the outgoing queue, the processor-to-memory bu er,
the memory-to-processor bu er and the processor, respectively. More precisely, let s be the
term
Sys(Msite(mem, min, mout), Site(id , cache, cin, cout, pmb, mpb, proc) j sites)
We de ne the following notations:
Mem(s) mem
Min(s) min
Mout(s) mout
Cache id(s) cache
Cin id(s) cin
Cout id(s) cout
Pmb id(s) pmb
Mpb id (s) mpb
Proc id(s) proc
We say a message is in transit from a cache to the memory if the message is in the cache's
outgoing queue or the memory's incoming queue. We say a message is in transit from the
memory to a cache if the message is in the memory's outgoing queue or the cache's incoming
queue. We use shorthand notation MoutCinid(s) to represent the messages in transit from the
memory to cache site id , and MinCoutid(s) the messages in transit from cache site id to the
memory. That is:
msg 2 MoutCin id(s) i msg 2 Mout(s) _ msg 2 Cin id (s)
msg 2 MinCout id(s) i msg 2 Min(s) _ msg 2 Cout id(s)
Let msg1 and msg2 be messages between the same source and destination regarding the same
address. We say messagemsg1 precedes message msg2 (or msg2 follows msg1), if the following
condition is satis ed:
msg1 and msg2 arebothinthesource's outgoing queue, and msg1 is in front ofmessage
msg2 or
msg1 and msg2 are both in the destination's incoming queue, and msg1 is in front of
message msg2 or
msg1 is in the destination's incoming queue and msg2 is in the source's outgoing queue.
We use notation msg" to represent that message msg has no preceding message, and notation
msg# to represent that message msg has no following message. Notation msg l means that
message msg has no preceding or following message (that is, it is the only message regarding
the address between the source and destination).
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