<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
GSAT	O
and	O
WalkSAT	B-Application
are	O
local	O
search	O
algorithms	O
to	O
solve	O
Boolean	O
satisfiability	O
problems	O
.	O
</s>
<s>
Both	O
algorithms	O
work	O
on	O
formulae	O
in	O
Boolean	O
logic	O
that	O
are	O
in	O
,	O
or	O
have	O
been	O
converted	O
into	O
conjunctive	B-Application
normal	I-Application
form	I-Application
.	O
</s>
<s>
If	O
the	O
assignment	O
satisfies	O
all	O
clauses	B-Application
,	O
the	O
algorithm	O
terminates	O
,	O
returning	O
the	O
assignment	O
.	O
</s>
<s>
Otherwise	O
,	O
a	O
variable	O
is	O
flipped	O
and	O
the	O
above	O
is	O
then	O
repeated	O
until	O
all	O
the	O
clauses	B-Application
are	O
satisfied	O
.	O
</s>
<s>
WalkSAT	B-Application
and	O
GSAT	O
differ	O
in	O
the	O
methods	O
used	O
to	O
select	O
which	O
variable	O
to	O
flip	O
.	O
</s>
<s>
GSAT	O
makes	O
the	O
change	O
which	O
minimizes	O
the	O
number	O
of	O
unsatisfied	O
clauses	B-Application
in	O
the	O
new	O
assignment	O
,	O
or	O
with	O
some	O
probability	O
picks	O
a	O
variable	O
at	O
random	O
.	O
</s>
<s>
WalkSAT	B-Application
first	O
picks	O
a	O
clause	O
which	O
is	O
unsatisfied	O
by	O
the	O
current	O
assignment	O
,	O
then	O
flips	O
a	O
variable	O
within	O
that	O
clause	O
.	O
</s>
<s>
The	O
clause	O
is	O
picked	O
at	O
random	O
among	O
unsatisfied	O
clauses	B-Application
.	O
</s>
<s>
The	O
variable	O
is	O
picked	O
that	O
will	O
result	O
in	O
the	O
fewest	O
previously	O
satisfied	O
clauses	B-Application
becoming	O
unsatisfied	O
,	O
with	O
some	O
probability	O
of	O
picking	O
one	O
of	O
the	O
variables	O
at	O
random	O
.	O
</s>
<s>
When	O
picking	O
at	O
random	O
,	O
WalkSAT	B-Application
is	O
guaranteed	O
at	O
least	O
a	O
chance	O
of	O
one	O
out	O
of	O
the	O
number	O
of	O
variables	O
in	O
the	O
clause	O
of	O
fixing	O
a	O
currently	O
incorrect	O
assignment	O
.	O
</s>
<s>
When	O
picking	O
a	O
guessed-to-be-optimal	O
variable	O
,	O
WalkSAT	B-Application
has	O
to	O
do	O
less	O
calculation	O
than	O
GSAT	O
because	O
it	O
is	O
considering	O
fewer	O
possibilities	O
.	O
</s>
<s>
Both	O
algorithms	O
may	O
restart	O
with	O
a	O
new	O
random	O
assignment	O
if	O
no	O
solution	O
has	O
been	O
found	O
for	O
too	O
long	O
,	O
as	O
a	O
way	O
of	O
getting	O
out	O
of	O
local	O
minima	O
of	O
numbers	O
of	O
unsatisfied	O
clauses	B-Application
.	O
</s>
<s>
Many	O
versions	O
of	O
GSAT	O
and	O
WalkSAT	B-Application
exist	O
.	O
</s>
<s>
WalkSAT	B-Application
has	O
been	O
proven	O
particularly	O
useful	O
in	O
solving	O
satisfiability	O
problems	O
produced	O
by	O
conversion	O
from	O
automated	B-Application
planning	I-Application
problems	O
.	O
</s>
<s>
The	O
approach	O
to	O
planning	O
that	O
converts	O
planning	O
problems	O
into	O
Boolean	O
satisfiability	O
problems	O
is	O
called	O
satplan	B-Application
.	O
</s>
<s>
MaxWalkSAT	B-Application
is	O
a	O
variant	O
of	O
WalkSAT	B-Application
designed	O
to	O
solve	O
the	O
weighted	B-Application
satisfiability	I-Application
problem	I-Application
,	O
in	O
which	O
each	O
clause	O
has	O
associated	O
with	O
a	O
weight	O
,	O
and	O
the	O
goal	O
is	O
to	O
find	O
an	O
assignment	O
—	O
one	O
which	O
may	O
or	O
may	O
not	O
satisfy	O
the	O
entire	O
formula	O
—	O
that	O
maximizes	O
the	O
total	O
weight	O
of	O
the	O
clauses	B-Application
satisfied	O
by	O
that	O
assignment	O
.	O
</s>
