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