Questionnaire-2024/bdds/ex2_sol.tex

\begin{cofactors}
$f$ \= $= (((a \lor \lnot b) \land \lnot (c \lor d)) \lor (a \land b))$\\
	\>$f_{a}$ \= $= (\lnot (c \lor d) \lor b)$\\
	\>\>$f_{ab}$ \= $= \true$\\
	\>\>$f_{a\lnot b}$ \= $= \lnot (c \lor d)$\\
	\>\>\>$f_{a\lnot bc}$ \= $= \false$\\
	\>\>\>$f_{a\lnot b\lnot c}$ \= $= \lnot d$\\
	\>\>\>\>$f_{a\lnot b\lnot cd}$ \= $= \false$\\
	\>\>\>\>$f_{a\lnot b\lnot c\lnot d}$ \= $= \true$\\
	%\>\>\>$f_{a\lnot b\lnot c}$ \= $= f_{a\lnot b}$\\
	\>$f_{\lnot a}$ \= $= (\lnot b \land \lnot (c \lor d))$\\
	\>\>$f_{\lnot ab}$ \= $= \false$\\
	\>\>$f_{\lnot a\lnot b}$ \= $= f_{a\lnot b}$\\
\end{cofactors}
The final ROBDD:
\begin{center}
\scalebox{0.75}{

\begin{tikzpicture}[>=latex,line join=bevel,]
  \pgfsetlinewidth{1bp}
%%
\pgfsetcolor{black}
  % Edge: f_E -> a0
  \draw [] (72.5bp,268.99bp) .. controls (72.5bp,258.92bp) and (72.5bp,243.47bp)  .. (72.5bp,233.3bp);
  % Edge: f_a -> b1
  \draw [] (123.5bp,210.99bp) .. controls (123.5bp,200.92bp) and (123.5bp,185.47bp)  .. (123.5bp,175.3bp);
  % Edge: f_a!b -> c2
  \draw [] (72.679bp,152.99bp) .. controls (72.859bp,142.92bp) and (73.134bp,127.47bp)  .. (73.316bp,117.3bp);
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (72.959bp,137.3bp) node {\Large$\bullet$};
  % Edge: f_a!b!c -> d3
  \draw [] (157.14bp,94.988bp) .. controls (151.54bp,84.544bp) and (142.84bp,68.308bp)  .. (137.42bp,58.183bp);
  \draw (146.86bp,75.812bp) node {\Large$\bullet$};
  % Edge: f_!a -> b4
  \draw [] (21.5bp,210.99bp) .. controls (21.5bp,200.92bp) and (21.5bp,185.47bp)  .. (21.5bp,175.3bp);
  \draw (21.5bp,195.3bp) node {\Large$\bullet$};
  % Edge: a0 -> b4
  \draw [] (65.409bp,213.21bp) .. controls (55.665bp,202.51bp) and (38.243bp,183.38bp)  .. (28.531bp,172.72bp);
  \draw (41.998bp,187.51bp) node {\Large$\bullet$};
  % Edge: a0 -> b1
  \draw [] (79.591bp,213.21bp) .. controls (89.335bp,202.51bp) and (106.76bp,183.38bp)  .. (116.47bp,172.72bp);
  % Edge: b4 -> c2
  \draw [] (28.73bp,155.21bp) .. controls (38.665bp,144.51bp) and (56.429bp,125.38bp)  .. (66.331bp,114.72bp);
  \draw (52.722bp,129.38bp) node {\Large$\circ$};
  % Edge: b4 -> 4
  \draw [] (21.5bp,152.99bp) .. controls (21.5bp,137.38bp) and (21.5bp,108.85bp)  .. (21.5bp,107.09bp);
  % Edge: b1 -> c2
  \draw [] (116.55bp,155.21bp) .. controls (107.0bp,144.51bp) and (89.915bp,125.38bp)  .. (80.393bp,114.72bp);
  \draw (93.714bp,129.64bp) node {\Large$\bullet$};
  % Edge: b1 -> 0
  \draw [] (123.32bp,152.99bp) .. controls (123.04bp,137.38bp) and (122.53bp,108.85bp)  .. (122.5bp,107.09bp);
  % Edge: c2 -> c2
  %\draw [] (81.517bp,113.81bp) .. controls (91.167bp,119.7bp) and (102.5bp,117.1bp)  .. (102.5bp,106.0bp) .. controls (102.5bp,94.898bp) and (91.167bp,92.297bp)  .. (81.517bp,98.194bp);
  %\draw (99.287bp,89.018bp) node {\Large$\bullet$};
  % Edge: c2 -> d3
  \draw [] (81.213bp,97.679bp) .. controls (92.583bp,86.887bp) and (113.71bp,66.836bp)  .. (124.97bp,56.146bp);
  \draw (110.47bp,69.914bp) node {\Large$\circ$};
  % Edge: c2 -> 1
  \draw [] (73.5bp,94.988bp) .. controls (73.5bp,79.384bp) and (73.5bp,50.854bp)  .. (73.5bp,49.086bp);
  % Edge: d3 -> 2
  \draw [] (130.28bp,36.791bp) .. controls (127.43bp,23.663bp) and (122.8bp,2.3815bp)  .. (122.51bp,1.0642bp);
  % Edge: d3 -> 3
  \draw [] (134.5bp,36.791bp) .. controls (137.07bp,23.663bp) and (141.23bp,2.3815bp)  .. (141.49bp,1.0642bp);
  \draw (137.65bp,20.692bp) node {\Large$\bullet$};
  % Node: f_E
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (94.0bp,291.0bp) -- (51.0bp,291.0bp) -- (51.0bp,269.0bp) -- (94.0bp,269.0bp) -- cycle;
  \draw (72.5bp,280.0bp) node {$f$};
\end{scope}
  % Node: a0
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (72.5bp,222.0bp) ellipse (11.0bp and 11.0bp);
  \draw (72.5bp,222.0bp) node {$a$};
\end{scope}
  % Node: f_a
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (145.0bp,233.0bp) -- (102.0bp,233.0bp) -- (102.0bp,211.0bp) -- (145.0bp,211.0bp) -- cycle;
  \draw (123.5bp,222.0bp) node {$f_{a}$};
\end{scope}
  % Node: b1
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (123.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
  \draw (123.5bp,164.0bp) node {$b$};
\end{scope}
  % Node: f_a!b
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (94.0bp,175.0bp) -- (51.0bp,175.0bp) -- (51.0bp,153.0bp) -- (94.0bp,153.0bp) -- cycle;
  \draw (72.5bp,164.0bp) node {$f_{a\lnot b}$};
\end{scope}
  % Node: c2
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (73.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
  \draw (73.5bp,106.0bp) node {$c$};
\end{scope}
  % Node: f_a!b!c
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (184.0bp,117.0bp) -- (141.0bp,117.0bp) -- (141.0bp,95.0bp) -- (184.0bp,95.0bp) -- cycle;
  \draw (162.5bp,106.0bp) node {$f_{a\lnot b\lnot c}$};
\end{scope}
  % Node: d3
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (132.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
  \draw (132.5bp,48.0bp) node {$d$};
\end{scope}
  % Node: f_!a
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (43.0bp,233.0bp) -- (0.0bp,233.0bp) -- (0.0bp,211.0bp) -- (43.0bp,211.0bp) -- cycle;
  \draw (21.5bp,222.0bp) node {$f_{\lnot a}$};
\end{scope}
  % Node: b4
\begin{scope}
  \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
  \pgfsetstrokecolor{strokecol}
  \draw (21.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
  \draw (21.5bp,164.0bp) node {$b$};
\end{scope}
%
\end{tikzpicture}


}
\end{center}