<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
a	O
node	B-Application
of	O
a	O
control-flow	O
graph	O
dominates	O
a	O
node	B-Application
if	O
every	O
path	O
from	O
the	O
entry	O
node	B-Application
to	O
must	O
go	O
through	O
.	O
</s>
<s>
By	O
definition	O
,	O
every	O
node	B-Application
dominates	O
itself	O
.	O
</s>
<s>
A	O
node	B-Application
strictly	O
dominates	O
a	O
node	B-Application
if	O
dominates	O
and	O
does	O
not	O
equal	O
.	O
</s>
<s>
The	O
immediate	O
dominator	B-Application
or	O
idom	O
of	O
a	O
node	B-Application
is	O
the	O
unique	O
node	B-Application
that	O
strictly	O
dominates	O
but	O
does	O
not	O
strictly	O
dominate	O
any	O
other	O
node	B-Application
that	O
strictly	O
dominates	O
.	O
</s>
<s>
Every	O
node	B-Application
,	O
except	O
the	O
entry	O
node	B-Application
,	O
has	O
an	O
immediate	O
dominator	B-Application
.	O
</s>
<s>
The	O
dominance	O
frontier	O
of	O
a	O
node	B-Application
is	O
the	O
set	O
of	O
all	O
nodes	O
such	O
that	O
dominates	O
an	O
immediate	O
predecessor	O
of	O
,	O
but	O
does	O
not	O
strictly	O
dominate	O
.	O
</s>
<s>
A	O
dominator	B-Application
tree	O
is	O
a	O
tree	O
where	O
each	O
node	B-Application
's	O
children	O
are	O
those	O
nodes	O
it	O
immediately	O
dominates	O
.	O
</s>
<s>
The	O
start	O
node	B-Application
is	O
the	O
root	O
of	O
the	O
tree	O
.	O
</s>
<s>
Dominators	B-Application
,	O
and	O
dominance	O
frontiers	O
particularly	O
,	O
have	O
applications	O
in	O
compilers	B-Language
for	O
computing	O
static	O
single	O
assignment	O
form	O
.	O
</s>
<s>
A	O
number	O
of	O
compiler	B-Language
optimizations	O
can	O
also	O
benefit	O
from	O
dominators	B-Application
.	O
</s>
<s>
The	O
flow	O
graph	O
in	O
this	O
case	O
comprises	O
basic	B-Application
blocks	I-Application
.	O
</s>
<s>
Memory	O
usage	O
analysis	O
can	O
benefit	O
from	O
the	O
dominator	B-Application
tree	O
to	O
easily	O
find	O
leaks	O
and	O
identify	O
high	O
memory	O
usage	O
.	O
</s>
<s>
In	O
hardware	O
systems	O
,	O
dominators	B-Application
are	O
used	O
for	O
computing	O
signal	O
probabilities	O
for	O
test	O
generation	O
,	O
estimating	O
switching	O
activities	O
for	O
power	O
and	O
noise	O
analysis	O
,	O
and	O
selecting	O
cut	O
points	O
in	O
equivalence	O
checking	O
.	O
</s>
<s>
Let	O
be	O
the	O
source	O
node	B-Application
on	O
the	O
Control-flow	O
graph	O
.	O
</s>
<s>
The	O
dominators	B-Application
of	O
a	O
node	B-Application
are	O
given	O
by	O
the	O
maximal	O
solution	O
to	O
the	O
following	O
data-flow	O
equations	O
:	O
</s>
<s>
The	O
dominator	B-Application
of	O
the	O
start	O
node	B-Application
is	O
the	O
start	O
node	B-Application
itself	O
.	O
</s>
<s>
The	O
set	O
of	O
dominators	B-Application
for	O
any	O
other	O
node	B-Application
is	O
the	O
intersection	O
of	O
the	O
set	O
of	O
dominators	B-Application
for	O
all	O
predecessors	O
of	O
.	O
</s>
<s>
The	O
node	B-Application
is	O
also	O
in	O
the	O
set	O
of	O
dominators	B-Application
for	O
.	O
</s>
<s>
Analogous	O
to	O
the	O
definition	O
of	O
dominance	O
above	O
,	O
a	O
node	B-Application
z	O
is	O
said	O
to	O
post-dominate	O
a	O
node	B-Application
n	O
if	O
all	O
paths	O
to	O
the	O
exit	O
node	B-Application
of	O
the	O
graph	O
starting	O
at	O
n	O
must	O
go	O
through	O
z	O
.	O
</s>
<s>
Similarly	O
,	O
the	O
immediate	O
post-dominator	O
of	O
a	O
node	B-Application
n	O
is	O
the	O
postdominator	O
of	O
n	O
that	O
does	O
n't	O
strictly	O
postdominate	O
any	O
other	O
strict	O
postdominators	O
of	O
n	O
.	O
</s>
