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38 lines
1.0 KiB
38 lines
1.0 KiB
\begin{cofactors}
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$f_{a}$ \= $= b \lor(c \biimp d)$ \\
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\>$f_{ab}$ \= $= \true $\\
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\>$f_{a\lnot b}$ \= $= c \biimp d$ \\
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\>\>$f_{a\lnot bc}$ \= $= d$ \\
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\>\>\>$f_{a\lnot b c d}$ \= $= \true$ \\
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\>\>\>$f_{a\lnot bc\lnot d}$ \= $= \false$ \\
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\>\>$f_{a\lnot b\lnot c}$ \= $= \lnot d = f_{abc}$ \\
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$f_{\lnot a}$ \= $=\true $
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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}
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\node[func node] (f) {$f$};
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\node[cofactor] (a1) [below of=f] {$a$};
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\node[phantom] (aR) [below right of=a1] {};
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\node[cofactor] (b1) [below left of=a1] {$b$};
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\node[phantom] (bL) [below left of=b1] {};
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\node[cofactor] (c1) [below right of=b1] {$c$};
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\node[cofactor] (d1) [below of=c1] {$d$};
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\node[phantom] (dL) [below left of=d1] {};
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\node[phantom] (dR) [below right of=d1] {};
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\funcEdge{f}{a1}
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\thenEdge{a1}{b1}
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\elseEdge{a1}{aR}
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\thenEdge{b1}{bL}
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\elseEdge{b1}{c1}
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\thenEdge[bend right]{c1}{d1}
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\negatedEdge[bend left]{c1}{d1}
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\thenEdge{d1}{dL}
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\elseEdge{d1}{dR}
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\end{bdd}
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\end{center}
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