<s>
In	O
logic	O
and	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
Davis	O
–	O
Putnam	O
–	O
Logemann	O
–	O
Loveland	O
(	O
DPLL	O
)	O
algorithm	O
is	O
a	O
complete	O
,	O
backtracking-based	O
search	B-Application
algorithm	I-Application
for	O
deciding	B-Algorithm
the	I-Algorithm
satisfiability	I-Algorithm
of	O
propositional	O
logic	O
formulae	O
in	O
conjunctive	B-Application
normal	I-Application
form	I-Application
,	O
i.e.	O
</s>
<s>
for	O
solving	O
the	O
CNF-SAT	B-Algorithm
problem	O
.	O
</s>
<s>
The	O
SAT	B-Algorithm
problem	I-Algorithm
is	O
important	O
both	O
from	O
theoretical	O
and	O
practical	O
points	O
of	O
view	O
.	O
</s>
<s>
In	O
complexity	O
theory	O
it	O
was	O
the	O
first	O
problem	O
proved	O
to	O
be	O
NP-complete	O
,	O
and	O
can	O
appear	O
in	O
a	O
broad	O
variety	O
of	O
applications	O
such	O
as	O
model	B-Application
checking	I-Application
,	O
automated	B-Application
planning	I-Application
and	I-Application
scheduling	I-Application
,	O
and	O
diagnosis	B-General_Concept
in	I-General_Concept
artificial	I-General_Concept
intelligence	I-General_Concept
.	O
</s>
<s>
As	O
such	O
,	O
writing	O
efficient	O
SAT	B-Application
solvers	I-Application
has	O
been	O
a	O
research	O
topic	O
for	O
many	O
years	O
.	O
</s>
<s>
GRASP	B-Application
(	O
1996-1999	O
)	O
was	O
an	O
early	O
implementation	O
using	O
DPLL	O
.	O
</s>
<s>
In	O
the	O
international	O
SAT	O
competitions	O
,	O
implementations	O
based	O
around	O
DPLL	O
such	O
as	O
zChaff	B-Application
and	O
MiniSat	O
were	O
in	O
the	O
first	O
places	O
of	O
the	O
competitions	O
in	O
2004	O
and	O
2005	O
.	O
</s>
<s>
Another	O
application	O
that	O
often	O
involves	O
DPLL	O
is	O
automated	B-Application
theorem	I-Application
proving	I-Application
or	O
satisfiability	B-Application
modulo	I-Application
theories	I-Application
(	O
SMT	O
)	O
,	O
which	O
is	O
a	O
SAT	B-Algorithm
problem	I-Algorithm
in	O
which	O
propositional	O
variables	O
are	O
replaced	O
with	O
formulas	O
of	O
another	O
mathematical	O
theory	O
.	O
</s>
<s>
The	O
basic	O
backtracking	B-Algorithm
algorithm	I-Algorithm
runs	O
by	O
choosing	O
a	O
literal	O
,	O
assigning	O
a	O
truth	O
value	O
to	O
it	O
,	O
simplifying	O
the	O
formula	O
and	O
then	O
recursively	O
checking	O
if	O
the	O
simplified	O
formula	O
is	O
satisfiable	O
;	O
if	O
this	O
is	O
the	O
case	O
,	O
the	O
original	O
formula	O
is	O
satisfiable	O
;	O
otherwise	O
,	O
the	O
same	O
recursive	O
check	O
is	O
done	O
assuming	O
the	O
opposite	O
truth	O
value	O
.	O
</s>
<s>
The	O
DPLL	B-Application
algorithm	I-Application
enhances	O
over	O
the	O
backtracking	B-Algorithm
algorithm	I-Algorithm
by	O
the	O
eager	O
use	O
of	O
the	O
following	O
rules	O
at	O
each	O
step	O
:	O
</s>
<s>
The	O
DPLL	B-Application
algorithm	I-Application
can	O
be	O
summarized	O
in	O
the	O
following	O
pseudocode	O
,	O
where	O
Φ	O
is	O
the	O
CNF	B-Application
formula	O
:	O
</s>
<s>
Either	O
the	O
CNF	B-Application
formula	O
Φ	O
is	O
empty	O
,	O
i.e.	O
,	O
it	O
contains	O
no	O
clause	O
.	O
</s>
<s>
The	O
Davis	O
–	O
Logemann	O
–	O
Loveland	O
algorithm	O
depends	O
on	O
the	O
choice	O
of	O
branching	O
literal	O
,	O
which	O
is	O
the	O
literal	O
considered	O
in	O
the	O
backtracking	B-Algorithm
step	O
.	O
</s>
<s>
Such	O
choice	O
functions	O
are	O
also	O
called	O
heuristic	B-Algorithm
functions	I-Algorithm
or	O
branching	O
heuristics	B-Algorithm
.	O
</s>
<s>
It	O
is	O
the	O
basis	O
for	O
almost	O
all	O
modern	O
SAT	B-Application
solvers	I-Application
.	O
</s>
<s>
It	O
does	O
not	O
use	O
learning	O
or	O
non-chronological	O
backtracking	B-Algorithm
(	O
introduced	O
in	O
1996	O
)	O
.	O
</s>
<s>
An	O
example	O
with	O
visualization	O
of	O
a	O
DPLL	B-Application
algorithm	I-Application
having	O
chronological	O
backtracking	B-Algorithm
:	O
</s>
<s>
Since	O
1986	O
,	O
(	O
Reduced	O
ordered	O
)	O
binary	B-Application
decision	I-Application
diagrams	I-Application
have	O
also	O
been	O
used	O
for	O
SAT	O
solving	O
.	O
</s>
<s>
DPLL	O
has	O
been	O
extended	O
for	O
automated	B-Application
theorem	I-Application
proving	I-Application
for	O
fragments	O
of	O
first-order	O
logic	O
by	O
way	O
of	O
the	O
DPLL(T )	O
algorithm	O
.	O
</s>
<s>
However	O
,	O
the	O
main	O
improvement	O
has	O
been	O
a	O
more	O
powerful	O
algorithm	O
,	O
Conflict-Driven	B-Application
Clause	I-Application
Learning	I-Application
(	O
CDCL	B-Application
)	O
,	O
which	O
is	O
similar	O
to	O
DPLL	O
but	O
after	O
reaching	O
a	O
conflict	O
"	O
learns	O
"	O
the	O
root	O
causes	O
(	O
assignments	O
to	O
variables	O
)	O
of	O
the	O
conflict	O
,	O
and	O
uses	O
this	O
information	O
to	O
perform	O
non-chronological	O
backtracking	B-Algorithm
(	O
aka	O
backjumping	B-Application
)	O
in	O
order	O
to	O
avoid	O
reaching	O
the	O
same	O
conflict	O
again	O
.	O
</s>
<s>
Most	O
state-of-the-art	O
SAT	B-Application
solvers	I-Application
are	O
based	O
on	O
the	O
CDCL	B-Application
framework	O
as	O
of	O
2019	O
.	O
</s>
