Questionnaire-2024/bdds/ex1_sol.tex

\begin{cofactors}
$f$ \= $= (((p \lor q) \land \lnot (p \land q)) \land r)$\\
	\>$f_{q}$ \= $= (\lnot (p \land q) \land r)$\\
	\>\>$f_{qp}$ \= $= \false$\\
	\>\>$f_{q\lnot p}$ \= $= r$\\
	\>\>\>$f_{q\lnot pr}$ \= $= \true$\\
	\>\>\>$f_{q\lnot p\lnot r}$ \= $= \false$\\
	\>$f_{\lnot q}$ \= $= (p \land r)$\\
	\>\>$f_{\lnot qp}$ \= $= f_{q\lnot p}$\\
	\>\>$f_{\lnot q\lnot p}$ \= $= \false$\\
\end{cofactors}
The final ROBDD: 
\begin{center}
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: f_E -> q0
  \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_q -> p1
  \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_q!p -> r2
  \draw [] (72.5bp,94.988bp) .. controls (72.5bp,84.921bp) and (72.5bp,69.474bp)  .. (72.5bp,59.304bp);
  % Edge: f_!q -> p3
  \draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp)  .. (21.5bp,117.3bp);
  % Edge: q0 -> p3
  \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: q0 -> p1
  \draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp)  .. (116.47bp,114.72bp);
  % Edge: p3 -> r2
  \draw [] (28.591bp,97.213bp) .. controls (38.335bp,86.514bp) and (55.757bp,67.385bp)  .. (65.469bp,56.72bp);
  % Edge: p3 -> 3
  \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: p1 -> r2
  \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: p1 -> 0
  \draw [] (123.5bp,94.988bp) .. controls (123.5bp,79.384bp) and (123.5bp,50.854bp)  .. (123.5bp,49.086bp);
  % Edge: r2 -> 1
  \draw [] (70.503bp,36.791bp) .. controls (67.934bp,23.663bp) and (63.77bp,2.3815bp)  .. (63.513bp,1.0642bp);
  % Edge: r2 -> 2
  \draw [] (74.719bp,36.791bp) .. controls (77.573bp,23.663bp) and (82.2bp,2.3815bp)  .. (82.486bp,1.0642bp);
  \draw (78.237bp,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: q0
\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 {$q$};
\end{scope}
  % Node: f_q
\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 {$f_{q}$};
\end{scope}
  % Node: p1
\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 {$p$};
\end{scope}
  % Node: f_q!p
\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 {$f_{q\lnot p}$};
\end{scope}
  % Node: r2
\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 {$r$};
\end{scope}
  % Node: f_!q
\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 {$f_{\lnot q}$};
\end{scope}
  % Node: p3
\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 {$p$};
\end{scope}
%
\end{tikzpicture}


}
\end{center}