Questionnaire-2024/bdds/1027_sol.tex

\begin{cofactors}
  $f$ \= $= ((\lnot x \land \lnot y) \lor (x \land y))$\\
    \>$f_{y}$ \= $= x$\\
    \>\>$f_{yx}$ \= $= \true$\\
    \>\>$f_{y\lnot x}$ \= $= \false$\\
    \>$f_{\lnot y}$ \= $= \lnot f_y$\\
  \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 [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp)  .. (21.5bp,117.3bp);
    % Edge: f_y -> x1
    \draw [] (63.382bp,94.988bp) .. controls (53.412bp,84.04bp) and (37.646bp,66.729bp)  .. (28.57bp,56.763bp);
    % Edge: y0 -> x1
    \draw [] (16.385bp,96.003bp) .. controls (14.19bp,85.491bp) and (14.205bp,68.213bp)  .. (16.429bp,57.79bp);
    % Edge: y0 -> x1
    \draw [] (26.615bp,96.003bp) .. controls (28.81bp,85.491bp) and (28.795bp,68.213bp)  .. (26.571bp,57.79bp);
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (30.134bp,77.47bp) node {\Large$\bullet$};
    % Edge: x1 -> 0
    \draw [] (19.503bp,36.791bp) .. controls (16.934bp,23.663bp) and (12.77bp,2.3815bp)  .. (12.513bp,1.0642bp);
    % Edge: x1 -> 1
    \draw [] (23.719bp,36.791bp) .. controls (26.573bp,23.663bp) and (31.2bp,2.3815bp)  .. (31.486bp,1.0642bp);
    \draw (27.237bp,20.608bp) node {\Large$\bullet$};
    % Node: f_E
  \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 {$f$};
  \end{scope}
    % Node: y0
  \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 {$y$};
  \end{scope}
    % Node: f_y
  \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 {$f_{y}$};
  \end{scope}
    % Node: x1
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (21.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (21.5bp,48.0bp) node {$x$};
  \end{scope}
  %
  \end{tikzpicture}
  
  
  }
  \end{center}