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115 lines
4.5 KiB
115 lines
4.5 KiB
\begin{cofactors}
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$f$ \= $= (((\lnot p \land q) \land r) \lor (p \land \lnot s))$\\
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\>$f_{p}$ \= $= \lnot s$\\
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\>\>$f_{ps}$ \= $= \false$\\
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\>\>$f_{p\lnot s}$ \= $= \true$\\
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\>$f_{\lnot p}$ \= $= (q \land r)$\\
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\>\>$f_{\lnot pq}$ \= $= r$\\
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\>\>\>$f_{\lnot pqr}$ \= $= \true$\\
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\>\>\>$f_{\lnot pq\lnot r}$ \= $= \false$\\
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\>\>$f_{\lnot p\lnot q}$ \= $= \false$\\
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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 -> p0
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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_p -> s1
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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_!p -> q2
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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: f_!pq -> r3
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\draw [] (70.712bp,94.988bp) .. controls (68.892bp,84.795bp) and (66.087bp,69.087bp) .. (64.272bp,58.925bp);
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% Edge: p0 -> q2
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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: p0 -> s1
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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: q2 -> r3
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\draw [] (27.55bp,96.737bp) .. controls (35.301bp,86.149bp) and (48.662bp,67.901bp) .. (56.425bp,57.297bp);
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% Edge: q2 -> 4
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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: r3 -> 2
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\draw [] (60.281bp,36.791bp) .. controls (57.427bp,23.663bp) and (52.8bp,2.3815bp) .. (52.514bp,1.0642bp);
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% Edge: r3 -> 3
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\draw [] (64.497bp,36.791bp) .. controls (67.066bp,23.663bp) and (71.23bp,2.3815bp) .. (71.487bp,1.0642bp);
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\draw (67.647bp,20.692bp) node {\Large$\bullet$};
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% Edge: s1 -> 0
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\draw [] (121.71bp,94.988bp) .. controls (118.93bp,79.384bp) and (113.83bp,50.854bp) .. (113.52bp,49.086bp);
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% Edge: s1 -> 1
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\draw [] (125.11bp,94.988bp) .. controls (127.62bp,79.384bp) and (132.2bp,50.854bp) .. (132.49bp,49.086bp);
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\draw (129.31bp,68.833bp) 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: p0
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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 {$p$};
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\end{scope}
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% Node: f_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 (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 {$f_{p}$};
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\end{scope}
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% Node: s1
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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 {$s$};
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\end{scope}
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% Node: f_!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 (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 {$f_{\lnot p}$};
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\end{scope}
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% Node: q2
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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 {$q$};
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\end{scope}
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% Node: f_!pq
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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 {$f_{\lnot pq}$};
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\end{scope}
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% Node: r3
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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 (62.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
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\draw (62.5bp,48.0bp) node {$r$};
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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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