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114 lines
4.3 KiB
114 lines
4.3 KiB
\begin{cofactors}
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$f$ \= $= (((p \lor q) \land \lnot (p \land q)) \land r)$\\
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\>$f_{q}$ \= $= (\lnot (p \land q) \land r)$\\
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\>\>$f_{qp}$ \= $= \false$\\
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\>\>$f_{q\lnot p}$ \= $= r$\\
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\>\>\>$f_{q\lnot pr}$ \= $= \true$\\
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\>\>\>$f_{q\lnot p\lnot r}$ \= $= \false$\\
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\>$f_{\lnot q}$ \= $= (p \land r)$\\
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\>\>$f_{\lnot qp}$ \= $= f_{q\lnot p}$\\
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\>\>$f_{\lnot q\lnot p}$ \= $= \false$\\
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\end{cofactors}
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The final ROBDD:
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\begin{center}
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\scalebox{0.75}{
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\begin{tikzpicture}[>=latex,line join=bevel,]
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\pgfsetlinewidth{1bp}
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%%
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\pgfsetcolor{black}
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% Edge: f_E -> q0
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\draw [] (72.5bp,210.99bp) .. controls (72.5bp,200.92bp) and (72.5bp,185.47bp) .. (72.5bp,175.3bp);
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (72.5bp,195.3bp) node {\Large$\bullet$};
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% Edge: f_q -> p1
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\draw [] (123.5bp,152.99bp) .. controls (123.5bp,142.92bp) and (123.5bp,127.47bp) .. (123.5bp,117.3bp);
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\draw (123.5bp,137.3bp) node {\Large$\bullet$};
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% Edge: f_q!p -> r2
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\draw [] (72.5bp,94.988bp) .. controls (72.5bp,84.921bp) and (72.5bp,69.474bp) .. (72.5bp,59.304bp);
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% Edge: f_!q -> p3
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\draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp) .. (21.5bp,117.3bp);
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% Edge: q0 -> p3
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\draw [] (65.409bp,155.21bp) .. controls (55.665bp,144.51bp) and (38.243bp,125.38bp) .. (28.531bp,114.72bp);
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\draw (41.998bp,129.51bp) node {\Large$\bullet$};
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% Edge: q0 -> p1
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\draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp) .. (116.47bp,114.72bp);
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% Edge: p3 -> r2
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\draw [] (28.591bp,97.213bp) .. controls (38.335bp,86.514bp) and (55.757bp,67.385bp) .. (65.469bp,56.72bp);
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% Edge: p3 -> 3
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\draw [] (21.5bp,94.988bp) .. controls (21.5bp,79.384bp) and (21.5bp,50.854bp) .. (21.5bp,49.086bp);
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\draw (21.5bp,69.086bp) node {\Large$\bullet$};
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% Edge: p1 -> r2
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\draw [] (116.41bp,97.213bp) .. controls (106.66bp,86.514bp) and (89.243bp,67.385bp) .. (79.531bp,56.72bp);
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\draw (92.998bp,71.507bp) node {\Large$\bullet$};
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% Edge: p1 -> 0
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\draw [] (123.5bp,94.988bp) .. controls (123.5bp,79.384bp) and (123.5bp,50.854bp) .. (123.5bp,49.086bp);
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% Edge: r2 -> 1
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\draw [] (70.503bp,36.791bp) .. controls (67.934bp,23.663bp) and (63.77bp,2.3815bp) .. (63.513bp,1.0642bp);
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% Edge: r2 -> 2
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\draw [] (74.719bp,36.791bp) .. controls (77.573bp,23.663bp) and (82.2bp,2.3815bp) .. (82.486bp,1.0642bp);
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\draw (78.237bp,20.608bp) node {\Large$\bullet$};
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% Node: f_E
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (94.0bp,233.0bp) -- (51.0bp,233.0bp) -- (51.0bp,211.0bp) -- (94.0bp,211.0bp) -- cycle;
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\draw (72.5bp,222.0bp) node {$f$};
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\end{scope}
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% Node: q0
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (72.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
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\draw (72.5bp,164.0bp) node {$q$};
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\end{scope}
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% Node: f_q
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (145.0bp,175.0bp) -- (102.0bp,175.0bp) -- (102.0bp,153.0bp) -- (145.0bp,153.0bp) -- cycle;
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\draw (123.5bp,164.0bp) node {$f_{q}$};
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\end{scope}
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% Node: p1
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (123.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
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\draw (123.5bp,106.0bp) node {$p$};
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\end{scope}
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% Node: f_q!p
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (94.0bp,117.0bp) -- (51.0bp,117.0bp) -- (51.0bp,95.0bp) -- (94.0bp,95.0bp) -- cycle;
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\draw (72.5bp,106.0bp) node {$f_{q\lnot p}$};
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\end{scope}
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% Node: r2
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (72.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
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\draw (72.5bp,48.0bp) node {$r$};
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\end{scope}
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% Node: f_!q
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (43.0bp,175.0bp) -- (0.0bp,175.0bp) -- (0.0bp,153.0bp) -- (43.0bp,153.0bp) -- cycle;
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\draw (21.5bp,164.0bp) node {$f_{\lnot q}$};
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\end{scope}
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% Node: p3
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (21.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
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\draw (21.5bp,106.0bp) node {$p$};
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\end{scope}
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%
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\end{tikzpicture}
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}
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\end{center}
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