Questionnaire-2024/bdds/0017_sol.tex

\begin{cofactors}
  $f$ \= $= (((a \land b) \lor (\lnot c \land d)) \lor (e \land \lnot a))$\\
    \>$f_{e}$ \= $= (((a \land b) \lor (\lnot c \land d)) \lor \lnot a)$\\
    \>\>$f_{ed}$ \= $= (((a \land b) \lor \lnot c) \lor \lnot a)$\\
    \>\>\>$f_{edc}$ \= $= ((a \land b) \lor \lnot a)$\\
    \>\>\>\>$f_{edcb}$ \= $= \true$\\
    \>\>\>\>$f_{edc\lnot b}$ \= $= \lnot a$\\
    \>\>\>\>\>$f_{edc\lnot ba}$ \= $= \false$\\
    \>\>\>\>\>$f_{edc\lnot b\lnot a}$ \= $= \true$\\
    \>\>\>$f_{ed\lnot c}$ \= $= \true$\\
    \>\>$f_{e\lnot d}$ \= $= f_{edc}$\\
    \>$f_{\lnot e}$ \= $= ((a \land b) \lor (\lnot c \land d))$\\
    \>\>$f_{\lnot ed}$ \= $= ((a \land b) \lor \lnot c)$\\
    \>\>\>$f_{\lnot edc}$ \= $= (a \land b)$\\
    \>\>\>\>$f_{\lnot edcb}$ \= $= \lnot f_{edc\lnot b}$\\
    \>\>\>\>$f_{\lnot edc\lnot b}$ \= $= \false$\\
    \>\>\>$f_{\lnot ed\lnot c}$ \= $= \true$\\
    \>\>$f_{\lnot e\lnot d}$ \= $= f_{\lnot edc}$\\
  \end{cofactors}
  The final ROBDD: 
  \begin{center}
  \scalebox{0.75}{
  
  \begin{tikzpicture}[>=latex,line join=bevel,]
    \pgfsetlinewidth{1bp}
  %%
  \pgfsetcolor{black}
    % Edge: f_E -> e0
    \draw [] (114.56bp,326.99bp) .. controls (114.56bp,316.92bp) and (114.56bp,301.47bp)  .. (114.56bp,291.3bp);
    % Edge: f_e -> d1
    \draw [] (195.56bp,268.99bp) .. controls (195.56bp,258.92bp) and (195.56bp,243.47bp)  .. (195.56bp,233.3bp);
    % Edge: f_ed -> c2
    \draw [] (145.63bp,210.99bp) .. controls (146.71bp,200.92bp) and (148.37bp,185.47bp)  .. (149.46bp,175.3bp);
    % Edge: f_edc -> b3
    \draw [] (236.62bp,152.99bp) .. controls (226.85bp,142.04bp) and (211.39bp,124.73bp)  .. (202.49bp,114.76bp);
    % Edge: f_edc!b -> a4
    \draw [] (144.56bp,94.988bp) .. controls (144.56bp,84.921bp) and (144.56bp,69.474bp)  .. (144.56bp,59.304bp);
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (144.56bp,79.304bp) node {\Large$\bullet$};
    % Edge: f_!e -> d5
    \draw [] (32.561bp,268.99bp) .. controls (32.561bp,258.92bp) and (32.561bp,243.47bp)  .. (32.561bp,233.3bp);
    % Edge: f_!ed -> c6
    \draw [] (83.74bp,210.99bp) .. controls (83.92bp,200.92bp) and (84.196bp,185.47bp)  .. (84.377bp,175.3bp);
    % Edge: f_!edc -> b7
    \draw [] (35.528bp,152.99bp) .. controls (37.53bp,142.8bp) and (40.616bp,127.09bp)  .. (42.612bp,116.93bp);
    % Edge: e0 -> d5
    \draw [] (105.79bp,273.01bp) .. controls (90.003bp,262.23bp) and (57.01bp,239.7bp)  .. (41.274bp,228.95bp);
    \draw (57.79bp,240.23bp) node {\Large$\circ$};
    % Edge: e0 -> d1
    \draw [] (123.23bp,273.01bp) .. controls (138.74bp,262.29bp) and (171.07bp,239.93bp)  .. (186.71bp,229.12bp);
    % Edge: d5 -> c6
    \draw [] (39.792bp,213.21bp) .. controls (49.726bp,202.51bp) and (67.49bp,183.38bp)  .. (77.392bp,172.72bp);
    % Edge: d5 -> b7
    \draw [] (25.112bp,213.55bp) .. controls (13.652bp,201.13bp) and (-6.1173bp,175.38bp)  .. (2.5613bp,153.0bp) .. controls (9.2091bp,135.86bp) and (25.549bp,121.2bp)  .. (35.777bp,113.28bp);
    \draw (20.122bp,125.73bp) node {\Large$\circ$};
    % Edge: c6 -> b7
    \draw [] (78.311bp,154.25bp) .. controls (70.753bp,143.67bp) and (58.116bp,125.98bp)  .. (50.636bp,115.51bp);
    % Edge: c6 -> 5
    \draw [] (84.561bp,152.99bp) .. controls (84.561bp,137.38bp) and (84.561bp,108.85bp)  .. (84.561bp,107.09bp);
    \draw (84.561bp,127.09bp) node {\Large$\circ$};
    % Edge: b7 -> a4
    \draw [] (53.79bp,99.832bp) .. controls (72.84bp,89.164bp) and (116.32bp,64.813bp)  .. (135.36bp,54.155bp);
    % Edge: b7 -> 4
    \draw [] (44.561bp,94.988bp) .. controls (44.561bp,79.384bp) and (44.561bp,50.854bp)  .. (44.561bp,49.086bp);
    \draw (44.561bp,69.086bp) node {\Large$\bullet$};
    % Edge: d1 -> c2
    \draw [] (188.92bp,212.74bp) .. controls (180.41bp,202.15bp) and (165.75bp,183.9bp)  .. (157.23bp,173.3bp);
    % Edge: d1 -> b3
    \draw [] (195.56bp,210.88bp) .. controls (195.56bp,189.3bp) and (195.56bp,138.96bp)  .. (195.56bp,117.26bp);
    \draw (195.56bp,137.26bp) node {\Large$\circ$};
    % Edge: c2 -> b3
    \draw [] (157.2bp,154.74bp) .. controls (165.71bp,144.15bp) and (180.37bp,125.9bp)  .. (188.89bp,115.3bp);
    % Edge: c2 -> 3
    \draw [] (143.77bp,154.74bp) .. controls (131.38bp,139.65bp) and (106.2bp,108.99bp)  .. (104.64bp,107.09bp);
    \draw (117.33bp,122.55bp) node {\Large$\circ$};
    % Edge: b3 -> a4
    \draw [] (188.47bp,97.213bp) .. controls (178.73bp,86.514bp) and (161.3bp,67.385bp)  .. (151.59bp,56.72bp);
    \draw (165.06bp,71.507bp) node {\Large$\bullet$};
    % Edge: b3 -> 0
    \draw [] (195.56bp,94.988bp) .. controls (195.56bp,79.384bp) and (195.56bp,50.854bp)  .. (195.56bp,49.086bp);
    % Edge: a4 -> 1
    \draw [] (142.56bp,36.791bp) .. controls (140.0bp,23.663bp) and (135.83bp,2.3815bp)  .. (135.57bp,1.0642bp);
    % Edge: a4 -> 2
    \draw [] (146.78bp,36.791bp) .. controls (149.63bp,23.663bp) and (154.26bp,2.3815bp)  .. (154.55bp,1.0642bp);
    \draw (150.3bp,20.608bp) node {\Large$\bullet$};
    % Node: f_E
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (136.06bp,349.0bp) -- (93.06bp,349.0bp) -- (93.06bp,327.0bp) -- (136.06bp,327.0bp) -- cycle;
    \draw (114.56bp,338.0bp) node {$f$};
  \end{scope}
    % Node: e0
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (114.56bp,280.0bp) ellipse (11.0bp and 11.0bp);
    \draw (114.56bp,280.0bp) node {$e$};
  \end{scope}
    % Node: f_e
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (217.06bp,291.0bp) -- (174.06bp,291.0bp) -- (174.06bp,269.0bp) -- (217.06bp,269.0bp) -- cycle;
    \draw (195.56bp,280.0bp) node {$f_{e}$};
  \end{scope}
    % Node: d1
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (195.56bp,222.0bp) ellipse (11.0bp and 11.0bp);
    \draw (195.56bp,222.0bp) node {$d$};
  \end{scope}
    % Node: f_ed
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (166.06bp,233.0bp) -- (123.06bp,233.0bp) -- (123.06bp,211.0bp) -- (166.06bp,211.0bp) -- cycle;
    \draw (144.56bp,222.0bp) node {$f_{ed}$};
  \end{scope}
    % Node: c2
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (150.56bp,164.0bp) ellipse (11.0bp and 11.0bp);
    \draw (150.56bp,164.0bp) node {$c$};
  \end{scope}
    % Node: f_edc
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (267.06bp,175.0bp) -- (224.06bp,175.0bp) -- (224.06bp,153.0bp) -- (267.06bp,153.0bp) -- cycle;
    \draw (245.56bp,164.0bp) node {$f_{edc}$};
  \end{scope}
    % Node: b3
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (195.56bp,106.0bp) ellipse (11.0bp and 11.0bp);
    \draw (195.56bp,106.0bp) node {$b$};
  \end{scope}
    % Node: f_edc!b
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (166.06bp,117.0bp) -- (123.06bp,117.0bp) -- (123.06bp,95.0bp) -- (166.06bp,95.0bp) -- cycle;
    \draw (144.56bp,106.0bp) node {$f_{edc\lnot b}$};
  \end{scope}
    % Node: a4
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (144.56bp,48.0bp) ellipse (11.0bp and 11.0bp);
    \draw (144.56bp,48.0bp) node {$a$};
  \end{scope}
    % Node: f_!e
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (54.06bp,291.0bp) -- (11.06bp,291.0bp) -- (11.06bp,269.0bp) -- (54.06bp,269.0bp) -- cycle;
    \draw (32.561bp,280.0bp) node {$f_{\lnot e}$};
  \end{scope}
    % Node: d5
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (32.56bp,222.0bp) ellipse (11.0bp and 11.0bp);
    \draw (32.561bp,222.0bp) node {$d$};
  \end{scope}
    % Node: f_!ed
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (105.06bp,233.0bp) -- (62.06bp,233.0bp) -- (62.06bp,211.0bp) -- (105.06bp,211.0bp) -- cycle;
    \draw (83.561bp,222.0bp) node {$f_{\lnot ed}$};
  \end{scope}
    % Node: c6
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (84.56bp,164.0bp) ellipse (11.0bp and 11.0bp);
    \draw (84.561bp,164.0bp) node {$c$};
  \end{scope}
    % Node: f_!edc
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (55.06bp,175.0bp) -- (12.06bp,175.0bp) -- (12.06bp,153.0bp) -- (55.06bp,153.0bp) -- cycle;
    \draw (33.561bp,164.0bp) node {$f_{\lnot edc}$};
  \end{scope}
    % Node: b7
  \begin{scope}
    \definecolor{strokecol}{rgb}{0.0,0.0,0.0};
    \pgfsetstrokecolor{strokecol}
    \draw (44.56bp,106.0bp) ellipse (11.0bp and 11.0bp);
    \draw (44.561bp,106.0bp) node {$b$};
  \end{scope}
  %
  \end{tikzpicture}
  
  
  }
  \end{center}