Questionnaire-2024/bdds/1028_sol.tex

\begin{cofactors}
  $f$ \= $= (((\lnot p \lor r) \land (q \lor \lnot p)) \land (\lnot q \lor p))$\\
    \>$f_{r}$ \= $= ((q \lor \lnot p) \land (\lnot q \lor p))$\\
    \>\>$f_{rq}$ \= $= p$\\
    \>\>\>$f_{rqp}$ \= $= \true$\\
    \>\>\>$f_{rq\lnot p}$ \= $= \false$\\
    \>\>$f_{r\lnot q}$ \= $= \lnot f_{rq}$\\
    \>$f_{\lnot r}$ \= $= ((\lnot p \land (q \lor \lnot p)) \land (\lnot q \lor p))$\\
    \>\>$f_{\lnot rq}$ \= $= \false$\\
    \>\>$f_{\lnot r\lnot q}$ \= $= (\lnot p \land \lnot p)$\\
    \>\>\>$f_{\lnot r\lnot qp}$ \= $= \false$\\
    \>\>\>$f_{\lnot r\lnot q\lnot p}$ \= $= \true$\\
  \end{cofactors}
  The final ROBDD: 
  \begin{center}
  \scalebox{0.75}{
  
  \begin{tikzpicture}[>=latex,line join=bevel,]
    \pgfsetlinewidth{1bp}
  %%
  \pgfsetcolor{black}
    % Edge: f_E -> r0
    \draw [] (72.5bp,210.99bp) .. controls (72.5bp,200.92bp) and (72.5bp,185.47bp)  .. (72.5bp,175.3bp);
    % Edge: f_r -> q1
    \draw [] (123.5bp,152.99bp) .. controls (123.5bp,142.92bp) and (123.5bp,127.47bp)  .. (123.5bp,117.3bp);
    % Edge: f_rq -> p2
    \draw [] (165.38bp,94.988bp) .. controls (155.41bp,84.04bp) and (139.65bp,66.729bp)  .. (130.57bp,56.763bp);
    % Edge: f_!r -> q3
    \draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp)  .. (21.5bp,117.3bp);
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (21.5bp,137.3bp) node {\Large$\bullet$};
    % Edge: f_!r!q -> p4
    \draw [] (70.712bp,94.988bp) .. controls (68.892bp,84.795bp) and (66.087bp,69.087bp)  .. (64.272bp,58.925bp);
    \draw (67.788bp,78.614bp) node {\Large$\bullet$};
    % Edge: r0 -> q3
    \draw [] (65.409bp,155.21bp) .. controls (55.665bp,144.51bp) and (38.243bp,125.38bp)  .. (28.531bp,114.72bp);
    \draw (41.998bp,129.51bp) node {\Large$\bullet$};
    % Edge: r0 -> q1
    \draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp)  .. (116.47bp,114.72bp);
    % Edge: q3 -> p4
    \draw [] (27.55bp,96.737bp) .. controls (35.301bp,86.149bp) and (48.662bp,67.901bp)  .. (56.425bp,57.297bp);
    \draw (44.611bp,73.434bp) node {\Large$\circ$};
    % Edge: q3 -> 2
    \draw [] (21.5bp,94.988bp) .. controls (21.5bp,79.384bp) and (21.5bp,50.854bp)  .. (21.5bp,49.086bp);
    % Edge: p4 -> 3
    \draw [] (60.281bp,36.791bp) .. controls (57.427bp,23.663bp) and (52.8bp,2.3815bp)  .. (52.514bp,1.0642bp);
    % Edge: p4 -> 4
    \draw [] (64.497bp,36.791bp) .. controls (67.066bp,23.663bp) and (71.23bp,2.3815bp)  .. (71.487bp,1.0642bp);
    \draw (67.647bp,20.692bp) node {\Large$\bullet$};
    % Edge: q1 -> p2
    \draw [] (118.39bp,96.003bp) .. controls (116.19bp,85.491bp) and (116.21bp,68.213bp)  .. (118.43bp,57.79bp);
    % Edge: q1 -> p2
    \draw [] (128.61bp,96.003bp) .. controls (130.81bp,85.491bp) and (130.79bp,68.213bp)  .. (128.57bp,57.79bp);
    \draw (132.13bp,77.47bp) node {\Large$\bullet$};
    % Edge: p2 -> 0
    \draw [] (121.28bp,36.791bp) .. controls (118.43bp,23.663bp) and (113.8bp,2.3815bp)  .. (113.51bp,1.0642bp);
    % Edge: p2 -> 1
    \draw [] (125.5bp,36.791bp) .. controls (128.07bp,23.663bp) and (132.23bp,2.3815bp)  .. (132.49bp,1.0642bp);
    \draw (128.65bp,20.692bp) node {\Large$\bullet$};
    % Node: f_E
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (94.0bp,233.0bp) -- (51.0bp,233.0bp) -- (51.0bp,211.0bp) -- (94.0bp,211.0bp) -- cycle;
    \draw (72.5bp,222.0bp) node {$f$};
  \end{scope}
    % Node: r0
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (72.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
    \draw (72.5bp,164.0bp) node {$r$};
  \end{scope}
    % Node: f_r
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (145.0bp,175.0bp) -- (102.0bp,175.0bp) -- (102.0bp,153.0bp) -- (145.0bp,153.0bp) -- cycle;
    \draw (123.5bp,164.0bp) node {$f_{r}$};
  \end{scope}
    % Node: q1
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (123.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
    \draw (123.5bp,106.0bp) node {$q$};
  \end{scope}
    % Node: f_rq
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (196.0bp,117.0bp) -- (153.0bp,117.0bp) -- (153.0bp,95.0bp) -- (196.0bp,95.0bp) -- cycle;
    \draw (174.5bp,106.0bp) node {$f_{rq}$};
  \end{scope}
    % Node: p2
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (123.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (123.5bp,48.0bp) node {$p$};
  \end{scope}
    % Node: f_!r
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (43.0bp,175.0bp) -- (0.0bp,175.0bp) -- (0.0bp,153.0bp) -- (43.0bp,153.0bp) -- cycle;
    \draw (21.5bp,164.0bp) node {$f_{\lnot r}$};
  \end{scope}
    % Node: q3
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (21.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
    \draw (21.5bp,106.0bp) node {$q$};
  \end{scope}
    % Node: f_!r!q
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (94.0bp,117.0bp) -- (51.0bp,117.0bp) -- (51.0bp,95.0bp) -- (94.0bp,95.0bp) -- cycle;
    \draw (72.5bp,106.0bp) node {$f_{\lnot r\lnot q}$};
  \end{scope}
    % Node: p4
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (62.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (62.5bp,48.0bp) node {$p$};
  \end{scope}
  %
  \end{tikzpicture}
  
  
  }
  \end{center}