Skip to content
GitLab
Projects
Groups
Snippets
/
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Sign in
Toggle navigation
Menu
Open sidebar
Martin Jonáš
DTEDI
Commits
4787b821
Commit
4787b821
authored
Sep 05, 2016
by
Martin Jonas
Browse files
Polishing
parent
cc7d22bb
Changes
1
Hide whitespace changes
Inline
Side-by-side
Chapters/Chapter02.tex
View file @
4787b821
...
...
@@ -85,7 +85,7 @@ and to each predicate symbol $P \in \Sigma^p$ of arity $n$ assigns a
relation
$
P
^
\mathcal
{
A
}
\subseteq
A
^
n
$
. Given a
$
\Sigma
$
-structure
$
\mathcal
{
A
}$
, there exists a unique homomorphic extension of
$
(
\_
)
^
\mathcal
{
A
}$
to
$
\Sigma
$
-terms, which to each
$
\Sigma
$
-term
$
t
$
assigns an element
$
t
^
\mathcal
{
A
}
\in
A
$
. In turn, using standard
assigns an element
$
t
^
\mathcal
{
A
}
\in
A
$
. In turn,
by
using standard
definitions, the assignment
$
(
\_
)
^
\mathcal
{
A
}$
can be further extended
to assign a truth value
$
\varphi
^
\mathcal
{
A
}
\in
\{
\true
,
\false
\}
$
to each
$
\Sigma
$
-formula
$
\varphi
$
. A
$
\Sigma
$
-structure
$
\mathcal
{
A
}$
...
...
@@ -159,9 +159,9 @@ signature, defined in the previous subsection, a \emph{many-sorted
modified. Arity of a symbol determines not only a number of its
arguments, but also their types -- each function symbol has assigned
$
(
n
+
1
)
$
-tuple of sort symbols for a non-negative integer
$
n
$
and each
predicate symbol
s
has assigned a
$
n
$
-tuple of sort symbols for a
predicate symbol has assigned a
$
n
$
-tuple of sort symbols for a
non-negative integer
$
n
$
. Simultaneous inductive definition of terms
of
a
sort
$
S
\in
\Sigma
^
S
$
and definitions of atoms, literals, clauses
of sort
s
$
S
\in
\Sigma
^
S
$
and definitions of atoms, literals, clauses
and formulas are straightforward and can be found for example in
Enderton~
\cite
{
End01
}
.
...
...
@@ -204,7 +204,7 @@ the other hand, if after elimination of all variables no clauses
remain, the formula is satisfiable. The main problem of
\dppr
is its
space complexity, since the number of the clauses may grow
exponentially even for simple formulas. To alleviate this problem, the
refinement of
\dppr
algorithm was introduced in 1962 by Davis,
refinement of
the
\dppr
algorithm was introduced in 1962 by Davis,
Logemann and Loveland~
\cite
{
DPLL62
}
.
The Davis--Putnam--Logemann--Loveland
\quotegraffito
{
If you don't know
...
...
Write
Preview
Supports
Markdown
0%
Try again
or
attach a new file
.
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment