Questionnaire-2024/bdds/1026_sol.tex

\begin{cofactors}
  $f$ \= $= ((\lnot x \lor \lnot y) \land (x \land (y \lor z)))$\\
    \>$f_{y}$ \= $= \false$\\
    \>$f_{\lnot y}$ \= $= (x \land z)$\\
    \>\>$f_{\lnot yz}$ \= $= x$\\
    \>\>\>$f_{\lnot yzx}$ \= $= \true$\\
    \>\>\>$f_{\lnot yz\lnot x}$ \= $= \false$\\
    \>\>$f_{\lnot y\lnot z}$ \= $= \false$\\
  \end{cofactors}
  The final ROBDD: 
  \begin{center}
  \scalebox{0.75}{
  
  \begin{tikzpicture}[>=latex,line join=bevel,]
    \pgfsetlinewidth{1bp}
  %%
  \pgfsetcolor{black}
    % Edge: f_E -> y0
    \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_!y -> z1
    \draw [] (25.254bp,152.99bp) .. controls (29.124bp,142.67bp) and (35.113bp,126.7bp)  .. (38.918bp,116.55bp);
    % Edge: f_!yz -> x2
    \draw [] (108.92bp,94.988bp) .. controls (105.24bp,84.669bp) and (99.535bp,68.698bp)  .. (95.911bp,58.551bp);
    % Edge: y0 -> z1
    \draw [] (67.68bp,154.0bp) .. controls (62.115bp,143.61bp) and (53.01bp,126.62bp)  .. (47.408bp,116.16bp);
    \draw (56.852bp,133.79bp) node {\Large$\bullet$};
    % Edge: y0 -> 0
    \draw [] (72.5bp,152.99bp) .. controls (72.5bp,137.38bp) and (72.5bp,108.85bp)  .. (72.5bp,107.09bp);
    % Edge: z1 -> x2
    \draw [] (49.452bp,97.213bp) .. controls (59.005bp,86.514bp) and (76.085bp,67.385bp)  .. (85.607bp,56.72bp);
    % Edge: z1 -> 3
    \draw [] (42.5bp,94.988bp) .. controls (42.5bp,79.384bp) and (42.5bp,50.854bp)  .. (42.5bp,49.086bp);
    \draw (42.5bp,69.086bp) node {\Large$\bullet$};
    % Edge: x2 -> 1
    \draw [] (90.503bp,36.791bp) .. controls (87.934bp,23.663bp) and (83.77bp,2.3815bp)  .. (83.513bp,1.0642bp);
    % Edge: x2 -> 2
    \draw [] (94.719bp,36.791bp) .. controls (97.573bp,23.663bp) and (102.2bp,2.3815bp)  .. (102.49bp,1.0642bp);
    \draw (98.237bp,20.608bp) 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: y0
  \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 {$y$};
  \end{scope}
    % Node: f_!y
  \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 {$f_{\lnot y}$};
  \end{scope}
    % Node: z1
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (42.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
    \draw (42.5bp,106.0bp) node {$z$};
  \end{scope}
    % Node: f_!yz
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (134.0bp,117.0bp) -- (91.0bp,117.0bp) -- (91.0bp,95.0bp) -- (134.0bp,95.0bp) -- cycle;
    \draw (112.5bp,106.0bp) node {$f_{\lnot yz}$};
  \end{scope}
    % Node: x2
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (92.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (92.5bp,48.0bp) node {$x$};
  \end{scope}
  %
  \end{tikzpicture}
  
  
  }
  \end{center}