|
|
\begin{cofactors} $f$ \= $= (((p \land q) \lor (r \land s)) \lor (\lnot p \land \lnot r))$\\ \>$f_{s}$ \= $= (((p \land q) \lor r) \lor (\lnot p \land \lnot r))$\\ \>\>$f_{sr}$ \= $= \true$\\ \>\>$f_{s\lnot r}$ \= $= ((p \land q) \lor \lnot p)$\\ \>\>\>$f_{s\lnot rq}$ \= $= \true$\\ \>\>\>$f_{s\lnot r\lnot q}$ \= $= \lnot p$\\ \>\>\>\>$f_{s\lnot r\lnot qp}$ \= $= \false$\\ \>\>\>\>$f_{s\lnot r\lnot q\lnot p}$ \= $= \true$\\ \>$f_{\lnot s}$ \= $= ((p \land q) \lor (\lnot p \land \lnot r))$\\ \>\>$f_{\lnot sr}$ \= $= (p \land q)$\\ \>\>\>$f_{\lnot srq}$ \= $= \lnot f_{s\lnot r\lnot q}$\\ \>\>\>$f_{\lnot sr\lnot q}$ \= $= \false$\\ \>\>$f_{\lnot s\lnot r}$ \= $= f_{s\lnot r}$\\ \end{cofactors} The final ROBDD: \begin{center} \scalebox{0.75}{ \begin{tikzpicture}[>=latex,line join=bevel,] \pgfsetlinewidth{1bp} %%
\pgfsetcolor{black} % Edge: f_E -> s0
\draw [] (123.5bp,268.99bp) .. controls (123.5bp,258.92bp) and (123.5bp,243.47bp) .. (123.5bp,233.3bp); % Edge: f_s -> r1
\draw [] (174.5bp,210.99bp) .. controls (174.5bp,200.92bp) and (174.5bp,185.47bp) .. (174.5bp,175.3bp); % Edge: f_s!r -> q2
\draw [] (123.5bp,152.99bp) .. controls (123.5bp,142.92bp) and (123.5bp,127.47bp) .. (123.5bp,117.3bp); % Edge: f_s!r!q -> p3
\draw [] (72.5bp,94.988bp) .. controls (72.5bp,84.921bp) and (72.5bp,69.474bp) .. (72.5bp,59.304bp); \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (72.5bp,79.304bp) node {\Large$\bullet$}; % Edge: f_!s -> r4
\draw [] (72.5bp,210.99bp) .. controls (72.5bp,200.92bp) and (72.5bp,185.47bp) .. (72.5bp,175.3bp); % Edge: f_!sr -> q5
\draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp) .. (21.5bp,117.3bp); % Edge: s0 -> r4
\draw [] (116.41bp,213.21bp) .. controls (106.66bp,202.51bp) and (89.243bp,183.38bp) .. (79.531bp,172.72bp); \draw (92.998bp,187.51bp) node {\Large$\circ$}; % Edge: s0 -> r1
\draw [] (130.59bp,213.21bp) .. controls (140.34bp,202.51bp) and (157.76bp,183.38bp) .. (167.47bp,172.72bp); % Edge: r4 -> q5
\draw [] (65.409bp,155.21bp) .. controls (55.665bp,144.51bp) and (38.243bp,125.38bp) .. (28.531bp,114.72bp); % Edge: r4 -> q2
\draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp) .. (116.47bp,114.72bp); \draw (103.0bp,129.51bp) node {\Large$\circ$}; % Edge: q5 -> p3
\draw [] (28.591bp,97.213bp) .. controls (38.335bp,86.514bp) and (55.757bp,67.385bp) .. (65.469bp,56.72bp); % Edge: q5 -> 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: r1 -> q2
\draw [] (167.41bp,155.21bp) .. controls (157.66bp,144.51bp) and (140.24bp,125.38bp) .. (130.53bp,114.72bp); \draw (144.0bp,129.51bp) node {\Large$\circ$}; % Edge: r1 -> 0
\draw [] (174.5bp,152.99bp) .. controls (174.5bp,137.38bp) and (174.5bp,108.85bp) .. (174.5bp,107.09bp); % Edge: q2 -> p3
\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: q2 -> 1
\draw [] (123.5bp,94.988bp) .. controls (123.5bp,79.384bp) and (123.5bp,50.854bp) .. (123.5bp,49.086bp); % Edge: p3 -> 2
\draw [] (70.281bp,36.791bp) .. controls (67.427bp,23.663bp) and (62.8bp,2.3815bp) .. (62.514bp,1.0642bp); % Edge: p3 -> 3
\draw [] (74.497bp,36.791bp) .. controls (77.066bp,23.663bp) and (81.23bp,2.3815bp) .. (81.487bp,1.0642bp); \draw (77.647bp,20.692bp) node {\Large$\bullet$}; % Node: f_E
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (145.0bp,291.0bp) -- (102.0bp,291.0bp) -- (102.0bp,269.0bp) -- (145.0bp,269.0bp) -- cycle; \draw (123.5bp,280.0bp) node {$f$}; \end{scope} % Node: s0
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (123.5bp,222.0bp) ellipse (11.0bp and 11.0bp); \draw (123.5bp,222.0bp) node {$s$}; \end{scope} % Node: f_s
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (196.0bp,233.0bp) -- (153.0bp,233.0bp) -- (153.0bp,211.0bp) -- (196.0bp,211.0bp) -- cycle; \draw (174.5bp,222.0bp) node {$f_{s}$}; \end{scope} % Node: r1
\begin{scope} \definecolor{strokecol}{rgb}{0.0,0.0,0.0}; \pgfsetstrokecolor{strokecol} \draw (174.5bp,164.0bp) ellipse (11.0bp and 11.0bp); \draw (174.5bp,164.0bp) node {$r$}; \end{scope} % Node: f_s!r
\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 {$f_{s\lnot r}$}; \end{scope} % Node: q2
\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_s!r!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 {$f_{s\lnot r\lnot q}$}; \end{scope} % Node: p3
\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 {$p$}; \end{scope} % Node: f_!s
\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 {$f_{\lnot s}$}; \end{scope} % Node: r4
\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 {$r$}; \end{scope} % Node: f_!sr
\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 {$f_{\lnot sr}$}; \end{scope} % Node: q5
\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}
|
