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57 lines
1.8 KiB
57 lines
1.8 KiB
$$f = (r \land \lnot p) \lor (r \land \lnot p) \lor (s \land \lnot r) \lor (\lnot s \land r)\lor (r \land q),$$
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\begin{cofactors}
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$f_{p}$ \= $= \lnot r \lor(s \land \lnot r) \lor (\lnot s \land r) \lor (r \land q)$ \\
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\>$f_{pq}$ \= $= \true$\\
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\>$f_{p\lnot q}$ \= $= r \lor (s \land \lnot r) \lor (\lnot s \land r)$\\
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\>\>$f_{p\lnot qr}$ \= $= \true$\\
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\>\>$f_{p\lnot q\lnot r}$ \= $= s$\\
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\>\>\>$f_{p\lnot q\lnot rs}$ \= $= \true$\\
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\>\>\>$f_{p\lnot q\lnot r\lnot s}$ \= $= \false$\\
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$f_{\lnot p}$ \= $= r \lor(s \land \lnot r) \lor (\lnot s \land r) \lor (r \land q)$ \\
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\>$f_{\lnot pq}$ \= $= r \lor(s \land \lnot r) \lor (\lnot s \land r)$ \\
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\>$f_{\lnot p\lnot q}$ \= $= r \lor(s \land \lnot r) \lor (\lnot s \land r)$ \\
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\>\>$\Rightarrow q$ does not have an influence on the formula. These cofactors can be skipped.\\
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\>$f_{\lnot pr}$ \= $= \true$ \\
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\>$f_{\lnot p\lnot r}$ \= $= s = f_{p\lnot q\lnot r}$ \\
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\end{cofactors}
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The final ROBDD:\\
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\begin{center}
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\begin{bdd}[4em]
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\node[func node] (f) {$f$};
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\node[cofactor] (p1) [below of=f] {$q$};
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\node[cofactor] (q1) [below left of=p1] {$q$};
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\node[cofactor] (r1) [below right of=p1] {$r$};
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\node[cofactor] (r2) [below right of=q1,yshift=-0.8em,xshift=-1.5em] {$r$};
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\node[phantom] (q1L) [below left of=q1] {};
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\node[phantom] (r1L) [below left of=r1] {};
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\node[cofactor] (s1) [below left of=r2] {$s$};
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\node[phantom] (r2L) [below left of=r2] {};
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\node[phantom] (r2R) [below right of=r2] {};
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\node[phantom] (s2L) [below left of=s1] {};
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\node[phantom] (s2R) [below right of=s1] {};
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\funcEdge{f}{p1}
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\thenEdge{p1}{q1}
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\elseEdge{p1}{r1}
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\thenEdge{q1}{q1L}
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\negatedEdge{q1}{r2}
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\thenEdge{r2}{s1}
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\negatedEdge{r2}{r2R}
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\thenEdge{r1}{r1L}
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\elseEdge[bend left]{r1}{s1}
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\thenEdge{s1}{s2L}
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\negatedEdge{s1}{s2R}
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\end{bdd}
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\end{center}
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