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Martin Jonáš
DTEDI
Commits
bcd1e724
Commit
bcd1e724
authored
Sep 05, 2016
by
Martin Jonas
Browse files
More polishing
parent
a6c04467
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2
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Chapters/Chapter02.tex
View file @
bcd1e724
...
...
@@ -312,13 +312,13 @@ combinations of the represented Boolean functions using the recursive
procedure
\texttt
{
Apply
}
~
\cite
{
Bry86
}
. The main idea of symbolic
\sat
solvers is to convert a
\cnf
formula to the corresponding
\robdd
and
check the root of the resulting
\bdd
. If the resulting
\bdd
is
equivalent to the
\bdd
for the
constant
$
0
$
function, the formula is
unsatisfiable, and it is satisfiable otherwise. However, in
order to
keep the size of the
\bdd
small, it is necessary to
existentially
quantify the variables during the computation. This
technique is known
as
\emph
{
early quantification
}
~
\cite
{
HKB96
}
. A
simplified symbolic
\sat
algorithm can be found for example in the
survey of
\sat
solving
by Darwiche and Pipatsriswat~
\cite
{
DP09
}
.
equivalent to the
\bdd
for the
function that is
$
0
$
everywhere, the
formula is
unsatisfiable, and it is satisfiable otherwise. However, in
order to
keep the size of the
\bdd
small, it is necessary to
existentially
quantify the variables during the computation. This
technique is known
as
\emph
{
early quantification
}
~
\cite
{
HKB96
}
. A
simplified symbolic
\sat
algorithm can be found for example in the
survey of
\sat
solving
by Darwiche and Pipatsriswat~
\cite
{
DP09
}
.
Look-ahead based algorithm, in contrast to the
\cdcl
, are employing
expensive heuristics to guide the
\dpll
search to a satisfying
...
...
Chapters/Chapter03.tex
View file @
bcd1e724
...
...
@@ -32,8 +32,8 @@ that at least one of the last 4 bits of the variable $a$ has to be
$
1
$
, i.e. the value of
$
a
$
is not divisible by
$
16
$
. After conjoining
this
\bdd
to the
\bdd
for
$
a
=
16
\cdot
b
\,
+
\,
16
\cdot
c
$
, the formula
is decided unsatisfiable, as the resulting
\bdd
represents the
constant
$
0
$
function
. On the other hand, if one considers
only
quantifier instantiations by the subterm of the input formula,
function that is
$
0
$
everywhere
. On the other hand, if one considers
only
quantifier instantiations by the subterm of the input formula,
exponentially many quantifier instances have to be added to the
formula to show its unsatisfiability, as there is no subterm of
$
\varphi
$
that can be instantiated as
$
x
$
to yield an unsatisfiable
...
...
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