<s>
In	O
computational	O
complexity	O
theory	O
,	O
a	O
branch	O
of	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
Max/min	B-Application
CSP/Ones	I-Application
classification	I-Application
theorems	I-Application
state	O
necessary	O
and	O
sufficient	O
conditions	O
that	O
determine	O
the	O
complexity	O
classes	O
of	O
problems	O
about	O
satisfying	O
a	O
subset	O
S	O
of	O
boolean	O
relations	O
.	O
</s>
<s>
They	O
are	O
similar	O
to	O
Schaefer	B-Application
's	I-Application
dichotomy	I-Application
theorem	I-Application
,	O
which	O
classifies	O
the	O
complexity	O
of	O
satisfying	O
finite	O
sets	O
of	O
relations	O
;	O
however	O
,	O
the	O
Max/min	B-Application
CSP/Ones	I-Application
classification	I-Application
theorems	I-Application
give	O
information	O
about	O
the	O
complexity	O
of	O
approximating	B-Algorithm
an	O
optimal	O
solution	O
to	O
a	O
problem	O
defined	O
by	O
S	O
.	O
</s>
<s>
Conjunctive	B-Application
normal	I-Application
form	I-Application
is	O
abbreviated	O
CNF	O
below	O
.	O
</s>
<s>
X(N )	O
OR-SAT	O
stands	O
for	O
a	O
satisfiability	B-Algorithm
problem	I-Algorithm
which	O
is	O
the	O
AND	O
of	O
several	O
boolean	O
linear	O
equations	O
that	O
can	O
be	O
written	O
as	O
XOR	O
clauses	O
.	O
</s>
<s>
Such	O
problems	O
are	O
APX-hard	B-Algorithm
but	O
with	O
an	O
factor	O
approximation	O
.	O
</s>
<s>
Such	O
problems	O
are	O
APX-hard	B-Algorithm
but	O
with	O
an	O
approximation	O
.	O
</s>
<s>
Min	O
Horn-Deletion-complete	O
is	O
yet	O
another	O
such	O
complexity	O
class	O
.	O
</s>
<s>
Such	O
problems	O
are	O
inapproximable	O
to	O
within	O
a	O
factor	O
for	O
some	O
,	O
but	O
are	O
in	O
Poly-APX	B-Algorithm
,	O
so	O
they	O
have	O
some	O
polynomial	O
factor	O
approximation	O
.	O
</s>
<s>
If	O
all	O
clauses	O
,	O
when	O
converted	O
to	O
disjunctive	B-Application
normal	I-Application
form	I-Application
,	O
have	O
two	O
terms	O
,	O
one	O
consisting	O
of	O
all	O
positive	O
(	O
unnegated	O
)	O
variables	O
and	O
the	O
other	O
all	O
negated	O
variables	O
,	O
it	O
is	O
in	O
PO	O
.	O
</s>
<s>
Otherwise	O
,	O
the	O
problem	O
is	O
APX-complete	B-Algorithm
.	O
</s>
<s>
If	O
each	O
clause	O
can	O
be	O
written	O
as	O
the	O
CNF	O
of	O
Dual-Horn	B-Application
subclauses	I-Application
,	O
it	O
is	O
in	O
PO	O
.	O
</s>
<s>
If	O
it	O
is	O
an	O
instance	O
of	O
X(N )	O
OR-SAT	O
but	O
not	O
2-X(N )	O
OR-SAT	O
,	O
it	O
is	O
APX-complete	B-Algorithm
.	O
</s>
<s>
If	O
each	O
clause	O
can	O
be	O
written	O
as	O
the	O
CNF	O
of	O
Horn	B-Application
subclauses	I-Application
,	O
it	O
is	O
Poly-APX-complete	O
.	O
</s>
<s>
If	O
it	O
is	O
an	O
instance	O
of	O
2-CNF-SAT	B-Application
,	O
it	O
is	O
Poly-APX-complete	O
.	O
</s>
<s>
If	O
setting	O
all	O
or	O
all	O
but	O
one	O
variable	O
false	O
satisfies	O
each	O
clause	O
,	O
it	O
is	O
Poly-APX-complete	O
.	O
</s>
<s>
If	O
all	O
clauses	O
,	O
when	O
converted	O
to	O
disjunctive	B-Application
normal	I-Application
form	I-Application
,	O
have	O
two	O
terms	O
,	O
one	O
consisting	O
of	O
all	O
positive	O
(	O
unnegated	O
)	O
variables	O
and	O
the	O
other	O
all	O
negated	O
variables	O
,	O
it	O
is	O
in	O
PO	O
.	O
</s>
<s>
If	O
all	O
clauses	O
are	O
the	O
OR	O
of	O
O(1 )	O
variables	O
,	O
it	O
is	O
APX-complete	B-Algorithm
.	O
</s>
<s>
If	O
it	O
is	O
an	O
instance	O
of	O
2-CNF-SAT	B-Application
,	O
it	O
is	O
Min	O
2CNF-Deletion-complete	O
.	O
</s>
<s>
If	O
all	O
clauses	O
are	O
Horn	B-Application
or	O
Dual-Horn	B-Application
,	O
it	O
is	O
Min	O
Horn	B-Application
Deletion-complete	O
.	O
</s>
<s>
If	O
each	O
clause	O
can	O
be	O
written	O
as	O
a	O
CNF	O
of	O
Horn	B-Application
subclauses	I-Application
,	O
it	O
is	O
in	O
PO	O
.	O
</s>
<s>
If	O
it	O
is	O
an	O
instance	O
of	O
2-CNF-SAT	B-Application
,	O
it	O
is	O
APX-complete	B-Algorithm
.	O
</s>
<s>
If	O
all	O
clauses	O
are	O
the	O
OR	O
of	O
O(1 )	O
variables	O
,	O
it	O
is	O
APX-complete	B-Algorithm
.	O
</s>
<s>
If	O
each	O
clause	O
can	O
be	O
written	O
as	O
a	O
CNF	O
of	O
Dual-Horn	B-Application
subclauses	I-Application
,	O
it	O
is	O
Min	O
Horn	B-Application
Deletion-complete	O
.	O
</s>
<s>
If	O
setting	O
all	O
variables	O
true	O
satisfies	O
all	O
clauses	O
,	O
it	O
is	O
Poly-APX-complete	O
.	O
</s>
