\begin{cofactors} $f$ \= $= ((((p \land q) \land \lnot r) \lor (\lnot q \land s)) \lor (\lnot p \land \lnot s))$\\ \>$f_{p}$ \= $= ((q \land \lnot r) \lor (\lnot q \land s))$\\ \>\>$f_{pq}$ \= $= \lnot r$\\ \>\>\>$f_{pqr}$ \= $= \false$\\ \>\>\>$f_{pq\lnot r}$ \= $= \true$\\ \>\>$f_{p\lnot q}$ \= $= s$\\ \>\>\>$f_{p\lnot qs}$ \= $= \true$\\ \>\>\>$f_{p\lnot q\lnot s}$ \= $= \false$\\ \>$f_{\lnot p}$ \= $= ((\lnot q \land s) \lor \lnot s)$\\ \>\>$f_{\lnot pq}$ \= $= \lnot f_{p\lnot q}$\\ \>\>$f_{\lnot p\lnot q}$ \= $= \true$\\ \end{cofactors} The final ROBDD: \begin{center} \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %% \pgfsetcolor{black} % Edge: f_E -> p0 \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_p -> q1 \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_pq -> r2 \draw [] (165.92bp,94.988bp) .. controls (156.53bp,84.04bp) and (141.7bp,66.729bp) .. (133.15bp,56.763bp); \draw (146.17bp,71.948bp) node {\Large$\bullet$}; % Edge: f_p!q -> s3 \draw [] (72.5bp,94.988bp) .. controls (72.5bp,84.921bp) and (72.5bp,69.474bp) .. (72.5bp,59.304bp); % Edge: f_!p -> q4 \draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp) .. (21.5bp,117.3bp); \draw (21.5bp,137.3bp) node {\Large$\bullet$}; % Edge: p0 -> q4 \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$\circ$}; % Edge: p0 -> q1 \draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp) .. (116.47bp,114.72bp); % Edge: q4 -> s3 \draw [] (28.591bp,97.213bp) .. controls (38.335bp,86.514bp) and (55.757bp,67.385bp) .. (65.469bp,56.72bp); % Edge: q4 -> 4 \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: q1 -> s3 \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: q1 -> r2 \draw [] (124.04bp,94.988bp) .. controls (124.58bp,84.921bp) and (125.4bp,69.474bp) .. (125.95bp,59.304bp); % Edge: s3 -> 2 \draw [] (71.168bp,36.791bp) .. controls (69.456bp,23.663bp) and (66.68bp,2.3815bp) .. (66.508bp,1.0642bp); % Edge: s3 -> 3 \draw [] (75.257bp,37.245bp) .. controls (78.954bp,24.164bp) and (85.101bp,2.4123bp) .. (85.481bp,1.0657bp); \draw (80.042bp,20.312bp) node {\Large$\bullet$}; % Edge: r2 -> 0 \draw [] (123.11bp,37.245bp) .. controls (118.56bp,24.164bp) and (110.99bp,2.4123bp) .. (110.52bp,1.0657bp); % Edge: r2 -> 1 \draw [] (127.17bp,36.791bp) .. controls (128.02bp,23.663bp) and (129.41bp,2.3815bp) .. (129.5bp,1.0642bp); \draw (128.19bp,21.022bp) 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: p0 \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 {$p$}; \end{scope} % Node: f_p \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 {$f_{p}$}; \end{scope} % Node: q1 \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 {$q$}; \end{scope} % Node: f_pq \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (196.0bp,117.0bp) -- (153.0bp,117.0bp) -- (153.0bp,95.0bp) -- (196.0bp,95.0bp) -- cycle; \draw (174.5bp,106.0bp) node {$f_{pq}$}; \end{scope} % Node: r2 \begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (126.5bp,48.0bp) ellipse (11.0bp and 11.0bp); \draw (126.5bp,48.0bp) node {$r$}; \end{scope} % Node: f_p!q \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 {$f_{p\lnot q}$}; \end{scope} % Node: s3 \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 {$s$}; \end{scope} % Node: f_!p \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 {$f_{\lnot p}$}; \end{scope} % Node: q4 \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 {$q$}; \end{scope} % \end{tikzpicture} } \end{center}