Questionnaire-2024/bdds/0014_sol.tex

\begin{cofactors}
  $f$ \= $= ((((p \land q) \land \lnot r) \lor (\lnot q \land s)) \lor (\lnot p \land \lnot s))$\\
    \>$f_{p}$ \= $= ((q \land \lnot r) \lor (\lnot q \land s))$\\
    \>\>$f_{pq}$ \= $= \lnot r$\\
    \>\>\>$f_{pqr}$ \= $= \false$\\
    \>\>\>$f_{pq\lnot r}$ \= $= \true$\\
    \>\>$f_{p\lnot q}$ \= $= s$\\
    \>\>\>$f_{p\lnot qs}$ \= $= \true$\\
    \>\>\>$f_{p\lnot q\lnot s}$ \= $= \false$\\
    \>$f_{\lnot p}$ \= $= ((\lnot q \land s) \lor \lnot s)$\\
    \>\>$f_{\lnot pq}$ \= $= \lnot f_{p\lnot q}$\\
    \>\>$f_{\lnot p\lnot q}$ \= $= \true$\\
  \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 [] (72.5bp,210.99bp) .. controls (72.5bp,200.92bp) and (72.5bp,185.47bp)  .. (72.5bp,175.3bp);
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (72.5bp,195.3bp) node {\Large$\bullet$};
    % Edge: f_p -> q1
    \draw [] (123.5bp,152.99bp) .. controls (123.5bp,142.92bp) and (123.5bp,127.47bp)  .. (123.5bp,117.3bp);
    \draw (123.5bp,137.3bp) node {\Large$\bullet$};
    % Edge: f_pq -> r2
    \draw [] (165.92bp,94.988bp) .. controls (156.53bp,84.04bp) and (141.7bp,66.729bp)  .. (133.15bp,56.763bp);
    \draw (146.17bp,71.948bp) node {\Large$\bullet$};
    % Edge: f_p!q -> s3
    \draw [] (72.5bp,94.988bp) .. controls (72.5bp,84.921bp) and (72.5bp,69.474bp)  .. (72.5bp,59.304bp);
    % Edge: f_!p -> q4
    \draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp)  .. (21.5bp,117.3bp);
    \draw (21.5bp,137.3bp) node {\Large$\bullet$};
    % Edge: p0 -> q4
    \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$\circ$};
    % Edge: p0 -> q1
    \draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp)  .. (116.47bp,114.72bp);
    % Edge: q4 -> s3
    \draw [] (28.591bp,97.213bp) .. controls (38.335bp,86.514bp) and (55.757bp,67.385bp)  .. (65.469bp,56.72bp);
    % Edge: q4 -> 4
    \draw [] (21.5bp,94.988bp) .. controls (21.5bp,79.384bp) and (21.5bp,50.854bp)  .. (21.5bp,49.086bp);
    \draw (21.5bp,69.086bp) node {\Large$\bullet$};
    % Edge: q1 -> s3
    \draw [] (116.41bp,97.213bp) .. controls (106.66bp,86.514bp) and (89.243bp,67.385bp)  .. (79.531bp,56.72bp);
    \draw (92.998bp,71.507bp) node {\Large$\bullet$};
    % Edge: q1 -> r2
    \draw [] (124.04bp,94.988bp) .. controls (124.58bp,84.921bp) and (125.4bp,69.474bp)  .. (125.95bp,59.304bp);
    % Edge: s3 -> 2
    \draw [] (71.168bp,36.791bp) .. controls (69.456bp,23.663bp) and (66.68bp,2.3815bp)  .. (66.508bp,1.0642bp);
    % Edge: s3 -> 3
    \draw [] (75.257bp,37.245bp) .. controls (78.954bp,24.164bp) and (85.101bp,2.4123bp)  .. (85.481bp,1.0657bp);
    \draw (80.042bp,20.312bp) node {\Large$\bullet$};
    % Edge: r2 -> 0
    \draw [] (123.11bp,37.245bp) .. controls (118.56bp,24.164bp) and (110.99bp,2.4123bp)  .. (110.52bp,1.0657bp);
    % Edge: r2 -> 1
    \draw [] (127.17bp,36.791bp) .. controls (128.02bp,23.663bp) and (129.41bp,2.3815bp)  .. (129.5bp,1.0642bp);
    \draw (128.19bp,21.022bp) 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: p0
  \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 {$p$};
  \end{scope}
    % Node: f_p
  \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 {$f_{p}$};
  \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_pq
  \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 {$f_{pq}$};
  \end{scope}
    % Node: r2
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (126.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (126.5bp,48.0bp) node {$r$};
  \end{scope}
    % Node: f_p!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 {$f_{p\lnot q}$};
  \end{scope}
    % Node: s3
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (72.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (72.5bp,48.0bp) node {$s$};
  \end{scope}
    % Node: f_!p
  \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 {$f_{\lnot p}$};
  \end{scope}
    % Node: q4
  \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}
  %
  \end{tikzpicture}
  
  
  }
  \end{center}