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71 lines
3.7 KiB
71 lines
3.7 KiB
DPLL algorithm:
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\scalebox{1}{
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\begin{tabular}{|l|c|c|c|c|c|c|c|c|}
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\hline
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Step & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \hline
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Decision Level & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 \\ \hline
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Assignment & - & $\lnot a$ & $\lnot a,c$ & $\lnot a,b,c$ & $\lnot a,b,c,e$ & - & $\lnot b$ & $\lnot b, f$ \\ \hline
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Cl. 1: $\lnot a,d$ & 1 & \cmark & \cmark & \cmark & \cmark & 1 & 1 & 1 \\ \hline
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Cl. 2: $\lnot d,c$ & 2 & 2 & \cmark & \cmark & \cmark & 2 & 2 & 2 \\ \hline
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Cl. 3: $\lnot b,e$ & 3 & 3 & 3 & $e$ & \cmark & 3 & \cmark & \cmark \\ \hline
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Cl. 4: $\lnot b,\lnot e$ & 4 & 4 & 4 & $\lnot e$ & $\{\}$ \xmark & 4 & \cmark & \cmark \\ \hline
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Cl. 5: $b,f$ & 5 & 5 & 5 & \cmark & \cmark & 5 & $f$ & \cmark \\ \hline
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Cl. 6: $b,\lnot f$ & 6 & 6 & 6 & \cmark & \cmark & 6 & $\lnot f$ & $\{\}$ \xmark \\ \hline
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\textcolor{gray}{Cl. 7: $\lnot b$} & - & - & - & - & learned $\lnot b$ & 7 & \cmark & \cmark \\ \hline \hline
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BCP & - & - & - & $e$ & - & $\lnot b$ & $f$ & - \\ \hline
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PL & $\lnot a$ & $c$ & - & - & - & - & - & - \\ \hline
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Decision & - & - & $b$ & - & - & - & - & UNSAT \\ \hline
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\end{tabular}}
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Ad 5:
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\begin{center}
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\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.5cm,
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thick,base node/.style={circle,draw,minimum size=20pt}, real node/.style={double,circle,draw,minimum size=20pt}]
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\node[base node] (1) {$b$};
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\node[base node] (2) [above right of=1] {$e$};
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\node[base node] (3) [below right of=1] {$\lnot e$};
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\node[base node] (4) [above right of=3] {$\bot$};
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\path[]
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(1) edge [] node {$3$} (2)
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edge [] node {$4$} (3)
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(2) edge [] node {} (4)
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(3) edge [] node {} (4);
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\end{tikzpicture}
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\end{center}
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\begin{prooftree}
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\AxiomC{$3. \; \lnot b \lor e$}
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\AxiomC{$4. \; \lnot b \lor \lnot e$}
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\BinaryInfC{$\lnot b$}
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\end{prooftree}
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Ad 8:
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\begin{center}
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\begin{tikzpicture}[->,>=stealth',shorten >=1pt,auto,node distance=1.5cm,
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thick,base node/.style={circle,draw,minimum size=20pt}, real node/.style={double,circle,draw,minimum size=20pt}]
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\node (0) {};
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\node[base node] (1) [right of=0] {$\lnot b$};
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\node[base node] (2) [above right of=1] {$f$};
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\node[base node] (3) [below right of=1] {$\lnot f$};
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\node[base node] (4) [above right of=3] {$\bot$};
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\path[]
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(0) edge [] node {$7$} (1)
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(1) edge [] node {$5$} (2)
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edge [] node {$6$} (3)
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(2) edge [] node {} (4)
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(3) edge [] node {} (4);
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\end{tikzpicture}
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\end{center}
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\begin{prooftree}
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\AxiomC{$5. \; b \lor f$}
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\AxiomC{$6. \; b \lor \lnot f$}
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\BinaryInfC{$b$}
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\AxiomC{$7. \; \lnot b$}
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\BinaryInfC{$\bot$}
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\end{prooftree}
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