Questionnaire-2024/bdds/0011_sol.tex

\begin{cofactors}
  $f$ \= $= (((p \land q) \lor (r \land \lnot s)) \lor ((\lnot p \land t) \land u))$\\
    \>$f_{p}$ \= $= (q \lor (r \land \lnot s))$\\
    \>\>$f_{pq}$ \= $= \true$\\
    \>\>$f_{p\lnot q}$ \= $= (r \land \lnot s)$\\
    \>\>\>$f_{p\lnot qr}$ \= $= \lnot s$\\
    \>\>\>\>$f_{p\lnot qrs}$ \= $= \false$\\
    \>\>\>\>$f_{p\lnot qr\lnot s}$ \= $= \true$\\
    \>\>\>$f_{p\lnot q\lnot r}$ \= $= \false$\\
    \>$f_{\lnot p}$ \= $= ((r \land \lnot s) \lor (t \land u))$\\
    \>\>$f_{\lnot pr}$ \= $= (\lnot s \lor (t \land u))$\\
    \>\>\>$f_{\lnot prs}$ \= $= (t \land u)$\\
    \>\>\>\>$f_{\lnot prst}$ \= $= u$\\
    \>\>\>\>\>$f_{\lnot prstu}$ \= $= \true$\\
    \>\>\>\>\>$f_{\lnot prst\lnot u}$ \= $= \false$\\
    \>\>\>\>$f_{\lnot prs\lnot t}$ \= $= \false$\\
    \>\>\>$f_{\lnot pr\lnot s}$ \= $= \true$\\
    \>\>$f_{\lnot p\lnot r}$ \= $= f_{\lnot prs}$\\
  \end{cofactors}
  The final ROBDD: 
  \begin{center}
  \scalebox{0.75}{
  
  \begin{tikzpicture}[>=latex,line join=bevel,]
    \pgfsetlinewidth{1bp}
  %%
  \pgfsetcolor{black}
    % Edge: f_E -> p0
    \draw [] (128.5bp,326.99bp) .. controls (128.5bp,316.92bp) and (128.5bp,301.47bp)  .. (128.5bp,291.3bp);
    % Edge: f_p -> q1
    \draw [] (174.49bp,268.99bp) .. controls (169.27bp,258.54bp) and (161.15bp,242.31bp)  .. (156.09bp,232.18bp);
    % Edge: f_p!q -> r2
    \draw [] (198.75bp,210.99bp) .. controls (194.88bp,200.67bp) and (188.89bp,184.7bp)  .. (185.08bp,174.55bp);
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (192.1bp,193.28bp) node {\Large$\bullet$};
    % Edge: f_p!qr -> s3
    \draw [] (231.61bp,152.99bp) .. controls (230.71bp,142.92bp) and (229.33bp,127.47bp)  .. (228.42bp,117.3bp);
    \draw (230.2bp,137.22bp) node {\Large$\bullet$};
    % Edge: f_!p -> r4
    \draw [] (82.685bp,268.99bp) .. controls (88.094bp,258.54bp) and (96.501bp,242.31bp)  .. (101.74bp,232.18bp);
    % Edge: f_!pr -> s5
    \draw [] (21.5bp,210.99bp) .. controls (21.5bp,200.92bp) and (21.5bp,185.47bp)  .. (21.5bp,175.3bp);
    % Edge: f_!prs -> t6
    \draw [] (73.394bp,152.99bp) .. controls (74.293bp,142.92bp) and (75.672bp,127.47bp)  .. (76.58bp,117.3bp);
    % Edge: f_!prst -> u7
    \draw [] (161.32bp,94.988bp) .. controls (155.91bp,84.544bp) and (147.5bp,68.308bp)  .. (142.26bp,58.183bp);
    % Edge: p0 -> r4
    \draw [] (124.77bp,269.5bp) .. controls (120.75bp,259.27bp) and (114.38bp,243.06bp)  .. (110.32bp,232.73bp);
    \draw (117.64bp,251.35bp) node {\Large$\circ$};
    % Edge: p0 -> q1
    \draw [] (132.4bp,269.5bp) .. controls (136.66bp,259.14bp) and (143.42bp,242.66bp)  .. (147.66bp,232.36bp);
    % Edge: r4 -> s5
    \draw [] (97.724bp,215.22bp) .. controls (81.436bp,204.49bp) and (46.704bp,181.6bp)  .. (30.356bp,170.83bp);
    % Edge: r4 -> t6
    \draw [] (107.27bp,210.63bp) .. controls (107.97bp,197.09bp) and (108.15bp,172.79bp)  .. (102.5bp,153.0bp) .. controls (98.455bp,138.84bp) and (89.518bp,124.18bp)  .. (83.501bp,115.32bp);
    \draw (94.602bp,131.96bp) node {\Large$\circ$};
    % Edge: s5 -> t6
    \draw [] (28.821bp,155.68bp) .. controls (39.494bp,145.01bp) and (59.224bp,125.28bp)  .. (69.998bp,114.5bp);
    % Edge: s5 -> 7
    \draw [] (21.5bp,152.99bp) .. controls (21.5bp,137.38bp) and (21.5bp,108.85bp)  .. (21.5bp,107.09bp);
    \draw (21.5bp,127.09bp) node {\Large$\circ$};
    % Edge: t6 -> u7
    \draw [] (85.344bp,97.679bp) .. controls (96.906bp,86.887bp) and (118.39bp,66.836bp)  .. (129.84bp,56.146bp);
    % Edge: t6 -> 6
    \draw [] (77.5bp,94.988bp) .. controls (77.5bp,79.384bp) and (77.5bp,50.854bp)  .. (77.5bp,49.086bp);
    \draw (77.5bp,69.086bp) node {\Large$\bullet$};
    % Edge: u7 -> 4
    \draw [] (135.28bp,36.791bp) .. controls (132.43bp,23.663bp) and (127.8bp,2.3815bp)  .. (127.51bp,1.0642bp);
    % Edge: u7 -> 5
    \draw [] (139.5bp,36.791bp) .. controls (142.07bp,23.663bp) and (146.23bp,2.3815bp)  .. (146.49bp,1.0642bp);
    \draw (142.65bp,20.692bp) node {\Large$\bullet$};
    % Edge: q1 -> r2
    \draw [] (156.32bp,212.0bp) .. controls (161.89bp,201.61bp) and (170.99bp,184.62bp)  .. (176.59bp,174.16bp);
    \draw (167.15bp,191.79bp) node {\Large$\bullet$};
    % Edge: q1 -> 0
    \draw [] (151.5bp,210.99bp) .. controls (151.5bp,195.38bp) and (151.5bp,166.85bp)  .. (151.5bp,165.09bp);
    % Edge: r2 -> s3
    \draw [] (188.29bp,154.74bp) .. controls (197.08bp,144.03bp) and (212.32bp,125.48bp)  .. (220.98bp,114.93bp);
    % Edge: r2 -> 3
    \draw [] (173.89bp,155.63bp) .. controls (164.66bp,146.64bp) and (148.71bp,130.93bp)  .. (135.5bp,117.0bp) .. controls (131.64bp,112.93bp) and (127.11bp,107.7bp)  .. (126.56bp,107.06bp);
    \draw (139.66bp,122.18bp) node {\Large$\circ$};
    % Edge: s3 -> 1
    \draw [] (225.71bp,94.988bp) .. controls (222.93bp,79.384bp) and (217.83bp,50.854bp)  .. (217.52bp,49.086bp);
    % Edge: s3 -> 2
    \draw [] (229.11bp,94.988bp) .. controls (231.62bp,79.384bp) and (236.2bp,50.854bp)  .. (236.49bp,49.086bp);
    \draw (233.31bp,68.833bp) node {\Large$\bullet$};
    % Node: f_E
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (150.0bp,349.0bp) -- (107.0bp,349.0bp) -- (107.0bp,327.0bp) -- (150.0bp,327.0bp) -- cycle;
    \draw (128.5bp,338.0bp) node {$f$};
  \end{scope}
    % Node: p0
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (128.5bp,280.0bp) ellipse (11.0bp and 11.0bp);
    \draw (128.5bp,280.0bp) node {$p$};
  \end{scope}
    % Node: f_p
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (201.0bp,291.0bp) -- (158.0bp,291.0bp) -- (158.0bp,269.0bp) -- (201.0bp,269.0bp) -- cycle;
    \draw (179.5bp,280.0bp) node {$f_{p}$};
  \end{scope}
    % Node: q1
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (151.5bp,222.0bp) ellipse (11.0bp and 11.0bp);
    \draw (151.5bp,222.0bp) node {$q$};
  \end{scope}
    % Node: f_p!q
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (224.0bp,233.0bp) -- (181.0bp,233.0bp) -- (181.0bp,211.0bp) -- (224.0bp,211.0bp) -- cycle;
    \draw (202.5bp,222.0bp) node {$f_{p\lnot q}$};
  \end{scope}
    % Node: r2
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (181.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
    \draw (181.5bp,164.0bp) node {$r$};
  \end{scope}
    % Node: f_p!qr
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (254.0bp,175.0bp) -- (211.0bp,175.0bp) -- (211.0bp,153.0bp) -- (254.0bp,153.0bp) -- cycle;
    \draw (232.5bp,164.0bp) node {$f_{p\lnot qr}$};
  \end{scope}
    % Node: s3
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (227.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
    \draw (227.5bp,106.0bp) node {$s$};
  \end{scope}
    % Node: f_!p
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (99.0bp,291.0bp) -- (56.0bp,291.0bp) -- (56.0bp,269.0bp) -- (99.0bp,269.0bp) -- cycle;
    \draw (77.5bp,280.0bp) node {$f_{\lnot p}$};
  \end{scope}
    % Node: r4
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (106.5bp,222.0bp) ellipse (11.0bp and 11.0bp);
    \draw (106.5bp,222.0bp) node {$r$};
  \end{scope}
    % Node: f_!pr
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (43.0bp,233.0bp) -- (0.0bp,233.0bp) -- (0.0bp,211.0bp) -- (43.0bp,211.0bp) -- cycle;
    \draw (21.5bp,222.0bp) node {$f_{\lnot pr}$};
  \end{scope}
    % Node: s5
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (21.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
    \draw (21.5bp,164.0bp) node {$s$};
  \end{scope}
    % Node: f_!prs
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (94.0bp,175.0bp) -- (51.0bp,175.0bp) -- (51.0bp,153.0bp) -- (94.0bp,153.0bp) -- cycle;
    \draw (72.5bp,164.0bp) node {$f_{\lnot prs}$};
  \end{scope}
    % Node: t6
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (77.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
    \draw (77.5bp,106.0bp) node {$t$};
  \end{scope}
    % Node: f_!prst
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (188.0bp,117.0bp) -- (145.0bp,117.0bp) -- (145.0bp,95.0bp) -- (188.0bp,95.0bp) -- cycle;
    \draw (166.5bp,106.0bp) node {$f_{\lnot prst}$};
  \end{scope}
    % Node: u7
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (137.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (137.5bp,48.0bp) node {$u$};
  \end{scope}
  %
  \end{tikzpicture}
  
  
  }
  \end{center}