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162 lines
6.8 KiB
162 lines
6.8 KiB
\begin{cofactors}
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$f$ \= $= (((q \land \lnot s) \lor (s \land (\lnot r \lor p))) \lor ((p \land q) \land r))$\\
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\>$f_{p}$ \= $= (((q \land \lnot s) \lor s) \lor (q \land r))$\\
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\>\>$f_{pq}$ \= $= \true$\\
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\>\>$f_{p\lnot q}$ \= $= s$\\
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\>\>\>$f_{p\lnot qs}$ \= $= \true$\\
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\>\>\>$f_{p\lnot q\lnot s}$ \= $= \false$\\
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\>$f_{\lnot p}$ \= $= ((q \land \lnot s) \lor (s \land \lnot r))$\\
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\>\>$f_{\lnot pq}$ \= $= (\lnot s \lor (s \land \lnot r))$\\
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\>\>\>$f_{\lnot pqr}$ \= $= \lnot f_{p\lnot q}$\\
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\>\>\>$f_{\lnot pq\lnot r}$ \= $= \true$\\
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\>\>$f_{\lnot p\lnot q}$ \= $= (s \land \lnot r)$\\
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\>\>\>$f_{\lnot p\lnot qr}$ \= $= \false$\\
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\>\>\>$f_{\lnot p\lnot q\lnot r}$ \= $= f_{p\lnot q}$\\
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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 [] (123.5bp,268.99bp) .. controls (123.5bp,258.92bp) and (123.5bp,243.47bp) .. (123.5bp,233.3bp);
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% Edge: f_p -> q1
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\draw [] (174.5bp,210.99bp) .. controls (174.5bp,200.92bp) and (174.5bp,185.47bp) .. (174.5bp,175.3bp);
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% Edge: f_p!q -> s2
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\draw [] (74.288bp,94.988bp) .. controls (76.108bp,84.795bp) and (78.913bp,69.087bp) .. (80.728bp,58.925bp);
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% Edge: f_!p -> q3
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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_!pq -> r4
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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!q -> r5
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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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\draw (21.5bp,137.3bp) node {\Large$\bullet$};
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% Edge: p0 -> q3
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\draw [] (116.41bp,213.21bp) .. controls (106.66bp,202.51bp) and (89.243bp,183.38bp) .. (79.531bp,172.72bp);
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\draw (92.998bp,187.51bp) node {\Large$\bullet$};
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% Edge: p0 -> q1
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\draw [] (130.59bp,213.21bp) .. controls (140.34bp,202.51bp) and (157.76bp,183.38bp) .. (167.47bp,172.72bp);
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% Edge: q3 -> r5
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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$\circ$};
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% Edge: q3 -> r4
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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: r5 -> s2
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\draw [] (29.226bp,97.908bp) .. controls (40.895bp,87.195bp) and (62.899bp,66.995bp) .. (74.644bp,56.212bp);
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\draw (59.911bp,69.737bp) node {\Large$\bullet$};
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% Edge: r5 -> 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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% Edge: r4 -> s2
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\draw [] (117.45bp,96.737bp) .. controls (109.7bp,86.149bp) and (96.338bp,67.901bp) .. (88.575bp,57.297bp);
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% Edge: r4 -> 3
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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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\draw (123.5bp,69.086bp) node {\Large$\bullet$};
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% Edge: q1 -> s2
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\draw [] (171.65bp,152.93bp) .. controls (167.29bp,138.85bp) and (157.95bp,113.01bp) .. (143.5bp,95.0bp) .. controls (128.72bp,76.585bp) and (105.0bp,61.54bp) .. (91.923bp,54.08bp);
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\draw (109.2bp,64.149bp) node {\Large$\circ$};
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% Edge: q1 -> 0
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\draw [] (177.46bp,153.25bp) .. controls (182.18bp,137.7bp) and (190.93bp,108.87bp) .. (191.47bp,107.09bp);
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% Edge: s2 -> 1
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\draw [] (80.281bp,36.791bp) .. controls (77.427bp,23.663bp) and (72.8bp,2.3815bp) .. (72.514bp,1.0642bp);
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% Edge: s2 -> 2
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\draw [] (84.497bp,36.791bp) .. controls (87.066bp,23.663bp) and (91.23bp,2.3815bp) .. (91.487bp,1.0642bp);
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\draw (87.647bp,20.692bp) 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 (145.0bp,291.0bp) -- (102.0bp,291.0bp) -- (102.0bp,269.0bp) -- (145.0bp,269.0bp) -- cycle;
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\draw (123.5bp,280.0bp) 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 (123.5bp,222.0bp) ellipse (11.0bp and 11.0bp);
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\draw (123.5bp,222.0bp) 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 (196.0bp,233.0bp) -- (153.0bp,233.0bp) -- (153.0bp,211.0bp) -- (196.0bp,211.0bp) -- cycle;
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\draw (174.5bp,222.0bp) node {$f_{p}$};
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\end{scope}
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% Node: q1
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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 (174.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
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\draw (174.5bp,164.0bp) node {$q$};
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\end{scope}
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% Node: f_p!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 (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 {$f_{p\lnot q}$};
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\end{scope}
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% Node: s2
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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 (82.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
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\draw (82.5bp,48.0bp) 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 (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 {$f_{\lnot p}$};
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\end{scope}
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% Node: q3
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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_!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 (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 {$f_{\lnot pq}$};
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\end{scope}
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% Node: r4
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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 {$r$};
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\end{scope}
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% Node: f_!p!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 {$f_{\lnot p\lnot q}$};
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\end{scope}
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% Node: r5
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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 {$r$};
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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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