Questionnaire-2024/bdds/0013_sol.tex

\begin{cofactors}
  $f$ \= $= (((\lnot p \land q) \land r) \lor (p \land \lnot s))$\\
    \>$f_{p}$ \= $= \lnot s$\\
    \>\>$f_{ps}$ \= $= \false$\\
    \>\>$f_{p\lnot s}$ \= $= \true$\\
    \>$f_{\lnot p}$ \= $= (q \land r)$\\
    \>\>$f_{\lnot pq}$ \= $= r$\\
    \>\>\>$f_{\lnot pqr}$ \= $= \true$\\
    \>\>\>$f_{\lnot pq\lnot r}$ \= $= \false$\\
    \>\>$f_{\lnot p\lnot q}$ \= $= \false$\\
  \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 -> s1
    \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_!p -> q2
    \draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp)  .. (21.5bp,117.3bp);
    % Edge: f_!pq -> r3
    \draw [] (70.712bp,94.988bp) .. controls (68.892bp,84.795bp) and (66.087bp,69.087bp)  .. (64.272bp,58.925bp);
    % Edge: p0 -> q2
    \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: p0 -> s1
    \draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp)  .. (116.47bp,114.72bp);
    % Edge: q2 -> r3
    \draw [] (27.55bp,96.737bp) .. controls (35.301bp,86.149bp) and (48.662bp,67.901bp)  .. (56.425bp,57.297bp);
    % Edge: q2 -> 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: r3 -> 2
    \draw [] (60.281bp,36.791bp) .. controls (57.427bp,23.663bp) and (52.8bp,2.3815bp)  .. (52.514bp,1.0642bp);
    % Edge: r3 -> 3
    \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: s1 -> 0
    \draw [] (121.71bp,94.988bp) .. controls (118.93bp,79.384bp) and (113.83bp,50.854bp)  .. (113.52bp,49.086bp);
    % Edge: s1 -> 1
    \draw [] (125.11bp,94.988bp) .. controls (127.62bp,79.384bp) and (132.2bp,50.854bp)  .. (132.49bp,49.086bp);
    \draw (129.31bp,68.833bp) 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: s1
  \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 {$s$};
  \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: q2
  \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_!pq
  \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 {$f_{\lnot pq}$};
  \end{scope}
    % Node: r3
  \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 {$r$};
  \end{scope}
  %
  \end{tikzpicture}
  
  
  }
  \end{center}