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9 lines
1.0 KiB
9 lines
1.0 KiB
\item \self In the following text fill the blanks with the missing word(s).
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The Graph Based Reduction is used to reduce a formula $\phi_{in}$ in \rule{4.5cm}{.4pt} \rule{5.5cm}{.4pt} to a formula in \rule{6cm}{.4pt} \rule{4cm}{.4pt} that is equisatisfiable.
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Two formulas are equisatisfiable if \rule{1cm}{.4pt} \rule{11cm}{.4pt}.
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In the first step of the algorithm, we create a Non-Polar Equality Graph and in the next step we make it chordal. The graph is chordal, if \rule{8.5cm}{.4pt} \rule{3.5cm}{.4pt}.
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We introduce fresh propositional variables for each equation to ensure \rule{4cm}{.4pt}.
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In order to ensure transitivity, the algorithm adds constraints of the form \rule{11cm}{.4pt} for all \rule{7cm}{.4pt} in the graph.
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The resulting equisatisfiable formula consists of two parts and is of the form: $\phi_{out} := \phi_{TC} $ \rule{0.5cm}{.4pt} $\hat{\phi_{in}}$.
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The right part of the formula $\hat{\phi_{in}}$ describes the flattening original formula in which we replace \rule{4cm}{.4pt} with \rule{6cm}{.4pt}.
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