<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
partial	B-Application
order	I-Application
reduction	I-Application
is	O
a	O
technique	O
for	O
reducing	O
the	O
size	O
of	O
the	O
state-space	B-Application
to	O
be	O
searched	O
by	O
a	O
model	B-Application
checking	I-Application
or	O
automated	B-Application
planning	I-Application
and	I-Application
scheduling	I-Application
algorithm	O
.	O
</s>
<s>
It	O
exploits	O
the	O
commutativity	O
of	O
concurrently	O
executed	O
transitions	B-General_Concept
that	O
result	O
in	O
the	O
same	O
state	O
when	O
executed	O
in	O
different	O
orders	O
.	O
</s>
<s>
In	O
explicit	O
state	O
space	O
exploration	O
,	O
partial	B-Application
order	I-Application
reduction	I-Application
usually	O
refers	O
to	O
the	O
specific	O
technique	O
of	O
expanding	O
a	O
representative	O
subset	O
of	O
all	O
enabled	O
transitions	B-General_Concept
.	O
</s>
<s>
This	O
technique	O
has	O
also	O
been	O
described	O
as	O
model	B-Application
checking	I-Application
with	O
representatives	O
.	O
</s>
<s>
Ample	O
sets	O
are	O
an	O
example	O
of	O
model	B-Application
checking	I-Application
with	O
representatives	O
.	O
</s>
<s>
Two	O
transitions	B-General_Concept
are	O
considered	O
independent	O
only	O
if	O
they	O
cannot	O
disable	O
another	O
whenever	O
they	O
are	O
mutually	O
enabled	O
.	O
</s>
<s>
Transitions	B-General_Concept
that	O
are	O
not	O
independent	O
,	O
are	O
dependent	O
.	O
</s>
<s>
Ample	O
sets	O
for	O
different	O
purposes	O
can	O
be	O
defined	O
by	O
giving	O
conditions	O
as	O
to	O
when	O
a	O
set	O
of	O
transitions	B-General_Concept
is	O
"	O
ample	O
"	O
in	O
a	O
given	O
state	O
.	O
</s>
<s>
Conditions	O
C0	O
and	O
C1	O
are	O
sufficient	O
for	O
preserving	O
all	O
the	O
deadlocks	B-Operating_System
in	O
the	O
state	O
space	O
.	O
</s>
<s>
D1	O
Either	O
is	O
a	O
deadlock	B-Operating_System
,	O
or	O
such	O
that	O
,	O
the	O
execution	O
of	O
is	O
possible	O
.	O
</s>
<s>
These	O
conditions	O
are	O
sufficient	O
for	O
preserving	O
all	O
deadlocks	B-Operating_System
,	O
just	O
like	O
C0	O
and	O
C1	O
are	O
in	O
the	O
ample	O
set	O
method	O
.	O
</s>
<s>
There	O
are	O
also	O
other	O
notations	O
for	O
partial	B-Application
order	I-Application
reduction	I-Application
.	O
</s>
<s>
In	O
symbolic	O
model	B-Application
checking	I-Application
,	O
partial	B-Application
order	I-Application
reduction	I-Application
can	O
be	O
achieved	O
by	O
adding	O
more	O
constraints	O
(	O
guard	O
strengthening	O
)	O
.	O
</s>
<s>
Further	O
applications	O
of	O
partial	B-Application
order	I-Application
reduction	I-Application
involve	O
automated	B-Application
planning	I-Application
.	O
</s>
