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38 lines
1.9 KiB
38 lines
1.9 KiB
\item \self Compute the propositional formula of the following circuit and transform it into an equisatisfiable formula in CNF by applying Tseitin's encoding.
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For each variable you introduce, clearly indicate which subformula of $\phi$ it represents.
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\tikzstyle{branch}=[fill,shape=circle,minimum size=3pt,inner sep=0pt]
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\begin{tikzpicture}[label distance=2mm]
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\node (a) at (0,0) {$a$};
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\node (b) at (0,-1) {$b$};
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\node (c) at (0,-2) {$c$};
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\node (z) at (10,-1) {$z$};
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\node (am) at (1,0) {};
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\node (cm) at (1,-2) {};
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\node (bm) at (3,-1) {};
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\node (not1m) at (3,-2) {};
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\node (not2m) at (5,-.5) {};
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\node (or1m) at (5,-1.5) {};
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\node (bc_c1) at (1,-1.1) {};
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\node (bc_c2) at (1.1,-1) {};
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\node (bc_c3) at (1,-.9) {};
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\node[and gate US, draw, logic gate inputs=nn] at ($(2,-.5)$) (and1) {\tiny AND};
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\node[not gate US, draw, logic gate inputs=n] at ($(2,-2)$) (not1) {\tiny NOT};
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\node[not gate US, draw, logic gate inputs=n] at ($(4,-.5)$) (not2) {\tiny NOT};
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\node[or gate US, draw, logic gate inputs=nn] at ($(4,-1.5)$) (or1) {\tiny OR};
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\node[and gate US, draw, logic gate inputs=nn] at ($(6,-1)$) (and2) {\tiny AND};
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\node[not gate US, draw, logic gate inputs=n] at ($(8,-1)$) (not3) {\tiny NOT};
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\draw (a.east) -| (am.center) |- (and1.input 1);
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\draw (c.east) -| (cm.center) node[circle, fill,inner sep=2pt] {} -- (bc_c1.center) -- (bc_c2.center) -- (bc_c3.center) |- (and1.input 2);
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\draw (b.east) -| (bm.center)|- (or1.input 1);
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\draw (c.east) -- (not1.input);
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\draw (and1.output) -- node[above] {$u$} (not2.input);
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\draw (not1.output) -| (not1m.center) node[below] {$v$} |- (or1.input 2);
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\draw (not2.output) -| (not2m.center) node[above] {$w$} |- (and2.input 1);
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\draw (or1.output) -| (or1m.center) node[below] {$x$} |- (and2.input 2);
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\draw (and2.output) -- node[below] {$y$} (not3.input);
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\draw (not3.output) -- (z.west);
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\end{tikzpicture}
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