Questionnaire-2024/bdds/0012_sol.tex

\begin{cofactors}
  $f$ \= $= (((p \land q) \lor (r \land s)) \lor (\lnot p \land \lnot r))$\\
    \>$f_{p}$ \= $= (q \lor (r \land s))$\\
    \>\>$f_{pq}$ \= $= \true$\\
    \>\>$f_{p\lnot q}$ \= $= (r \land s)$\\
    \>\>\>$f_{p\lnot qr}$ \= $= s$\\
    \>\>\>\>$f_{p\lnot qrs}$ \= $= \true$\\
    \>\>\>\>$f_{p\lnot qr\lnot s}$ \= $= \false$\\
    \>\>\>$f_{p\lnot q\lnot r}$ \= $= \false$\\
    \>$f_{\lnot p}$ \= $= ((r \land s) \lor \lnot r)$\\
    \>\>$f_{\lnot pr}$ \= $= f_{p\lnot qr}$\\
    \>\>$f_{\lnot p\lnot r}$ \= $= \true$\\
  \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 [] (76.036bp,268.99bp) .. controls (76.036bp,258.92bp) and (76.036bp,243.47bp)  .. (76.036bp,233.3bp);
    % Edge: f_p -> q1
    \draw [] (126.5bp,210.99bp) .. controls (125.96bp,200.92bp) and (125.13bp,185.47bp)  .. (124.59bp,175.3bp);
    % Edge: f_p!q -> r2
    \draw [] (171.28bp,152.99bp) .. controls (167.41bp,142.67bp) and (161.42bp,126.7bp)  .. (157.62bp,116.55bp);
    % Edge: f_p!qr -> s3
    \draw [] (84.036bp,94.988bp) .. controls (84.036bp,84.921bp) and (84.036bp,69.474bp)  .. (84.036bp,59.304bp);
    % Edge: f_!p -> r4
    \draw [] (26.109bp,210.99bp) .. controls (27.188bp,200.92bp) and (28.843bp,185.47bp)  .. (29.932bp,175.3bp);
    % Edge: p0 -> r4
    \draw [] (69.397bp,212.74bp) .. controls (60.889bp,202.15bp) and (46.225bp,183.9bp)  .. (37.704bp,173.3bp);
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (50.231bp,188.89bp) node {\Large$\circ$};
    % Edge: p0 -> q1
    \draw [] (82.711bp,213.21bp) .. controls (91.778bp,202.63bp) and (107.91bp,183.81bp)  .. (117.11bp,173.08bp);
    % Edge: r4 -> s3
    \draw [] (33.339bp,152.98bp) .. controls (36.665bp,139.41bp) and (43.48bp,114.64bp)  .. (53.036bp,95.0bp) .. controls (59.948bp,80.799bp) and (70.727bp,65.915bp)  .. (77.581bp,57.05bp);
    % Edge: r4 -> 4
    \draw [] (26.743bp,153.75bp) .. controls (19.589bp,138.34bp) and (5.9248bp,108.91bp)  .. (5.0778bp,107.09bp);
    \draw (13.5bp,125.23bp) node {\Large$\circ$};
    % Edge: q1 -> r2
    \draw [] (128.86bp,154.0bp) .. controls (134.42bp,143.61bp) and (143.53bp,126.62bp)  .. (149.13bp,116.16bp);
    \draw (139.68bp,133.79bp) node {\Large$\circ$};
    % Edge: q1 -> 0
    \draw [] (124.04bp,152.99bp) .. controls (124.04bp,137.38bp) and (124.04bp,108.85bp)  .. (124.04bp,107.09bp);
    % Edge: r2 -> s3
    \draw [] (145.73bp,98.356bp) .. controls (132.26bp,87.578bp) and (105.8bp,66.407bp)  .. (92.33bp,55.635bp);
    % Edge: r2 -> 3
    \draw [] (154.04bp,94.988bp) .. controls (154.04bp,79.384bp) and (154.04bp,50.854bp)  .. (154.04bp,49.086bp);
    \draw (154.04bp,69.086bp) node {\Large$\bullet$};
    % Edge: s3 -> 1
    \draw [] (82.039bp,36.791bp) .. controls (79.47bp,23.663bp) and (75.307bp,2.3815bp)  .. (75.049bp,1.0642bp);
    % Edge: s3 -> 2
    \draw [] (86.256bp,36.791bp) .. controls (89.11bp,23.663bp) and (93.736bp,2.3815bp)  .. (94.023bp,1.0642bp);
    \draw (89.774bp,20.608bp) node {\Large$\bullet$};
    % Node: f_E
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (97.54bp,291.0bp) -- (54.54bp,291.0bp) -- (54.54bp,269.0bp) -- (97.54bp,269.0bp) -- cycle;
    \draw (76.036bp,280.0bp) node {$f$};
  \end{scope}
    % Node: p0
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (76.04bp,222.0bp) ellipse (11.0bp and 11.0bp);
    \draw (76.036bp,222.0bp) node {$p$};
  \end{scope}
    % Node: f_p
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (148.54bp,233.0bp) -- (105.54bp,233.0bp) -- (105.54bp,211.0bp) -- (148.54bp,211.0bp) -- cycle;
    \draw (127.04bp,222.0bp) node {$f_{p}$};
  \end{scope}
    % Node: q1
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (124.04bp,164.0bp) ellipse (11.0bp and 11.0bp);
    \draw (124.04bp,164.0bp) node {$q$};
  \end{scope}
    % Node: f_p!q
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (196.54bp,175.0bp) -- (153.54bp,175.0bp) -- (153.54bp,153.0bp) -- (196.54bp,153.0bp) -- cycle;
    \draw (175.04bp,164.0bp) node {$f_{p\lnot q}$};
  \end{scope}
    % Node: r2
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (154.04bp,106.0bp) ellipse (11.0bp and 11.0bp);
    \draw (154.04bp,106.0bp) node {$r$};
  \end{scope}
    % Node: f_p!qr
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (105.54bp,117.0bp) -- (62.54bp,117.0bp) -- (62.54bp,95.0bp) -- (105.54bp,95.0bp) -- cycle;
    \draw (84.036bp,106.0bp) node {$f_{p\lnot qr}$};
  \end{scope}
    % Node: s3
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (84.04bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (84.036bp,48.0bp) node {$s$};
  \end{scope}
    % Node: f_!p
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (46.54bp,233.0bp) -- (3.54bp,233.0bp) -- (3.54bp,211.0bp) -- (46.54bp,211.0bp) -- cycle;
    \draw (25.036bp,222.0bp) node {$f_{\lnot p}$};
  \end{scope}
    % Node: r4
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (31.04bp,164.0bp) ellipse (11.0bp and 11.0bp);
    \draw (31.036bp,164.0bp) node {$r$};
  \end{scope}
  %
  \end{tikzpicture}
  
  
  }
  \end{center}