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Resolutionsalgorithmus

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Martin Thoma 2013-09-07 14:46:54 +02:00
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source-code/Pseudocode/Resolutionsalgorithmus/Resolutionsalgorithmus.tex Normal file
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\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[ngerman]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf
\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
\usepackage{braket} % needed for \Set
\usepackage{algorithm,algpseudocode}
\algnewcommand\True{\textbf{true}\space}
\algnewcommand\False{\textbf{false}\space}
\algnewcommand{\LineComment}[1]{\State \(\triangleright\) #1}
\begin{document}
\begin{preview}
\begin{algorithm}[H]
\begin{algorithmic}
\Require Klauselmenge $K$ in KNF (jede Klausel wird durch ein mit den
Werten $\Set{-1,0,1}$ Array
repräsentiert, dessen Länge gleich der Anzahl $n$ der Symbole ist),\\
zu beweisende Aussage ist $\alpha$,\\
$\beta := \neg \alpha$ in KNF
\Procedure{Resolutionsalgorithmus}{$K$, $\beta$}
\State $\gamma \gets K \cup \Set{\beta}$
\State $foundMatch \gets$ \True
\While{$foundMatch$}
\State $foundMatch \gets$ \False
\LineComment{Finde zwei Klauseln, bei denen ein Symbol verneint bzw. nicht-verneint vorkommt. Wende darauf die Resolutionsregel an}
\For{$i \in \Set{1, \dots, |\gamma|-1}$}
\For{$j \in \Set{i+1, \dots |\gamma|}$}
\For{$k \in \Set{0, \dots, n-1}$}
\If{$\gamma_i[k] \cdot \gamma_j[k] == (-1)$}
\State $foundMatch \gets$ \True
\State $tmp \gets $ Array der Länge $n$
\For{$l \in \Set{0, \dots, n-1}$}
\If{$\gamma_i[l] \cdot \gamma_j[l] == (-1)$ and
$l \neq k$}
\State $tmp \gets $ leere Klausel
\State break
\ElsIf{$\gamma_i[l] \neq 0$}
\State $tmp[l] \gets \gamma_i[l]$
\Else
\State $tmp[l] \gets \gamma_j[l]$
\EndIf
\EndFor
\State $\gamma \gets (\gamma \cup \Set{tmp}) \setminus
\Set{\gamma_i, \gamma_j}$
\State break
\EndIf
\EndFor
\If{$foundMatch$}
\State break
\EndIf
\EndFor
\If{$foundMatch$}
\State break
\EndIf
\EndFor
\EndWhile
\EndProcedure
\end{algorithmic}
\caption{Resolutionsalgorithmus}
\label{alg:resolutionsalgorithmus}
\end{algorithm}
\end{preview}
\end{document}