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Small Formulas for Large Programs: On-line Constraint ...

Small Formulas for Large Programs: On-line Constraint ...

Algorithm ● Definition

Algorithm ● Definition of simplified form suggests trivial algorithm: – Pick any leaf, replace it by true/false. – Check if formula is equivalent. – Repeat until no leaf can be replaced. ● Requires repeatedly checking satisfiability of formulas twice as large as the original formula. ● But we can do better than this naïve algorithm!

Critical Constraint Idea: Compute a constraint C, called critical constraint, for each leaf L such that: (i) L is non­constraining iff (ii) L is non­ relaxing iff Intuitively, C describes the condition under which L determines whether an assignment satisfies the formula. C ) L C ) :L C is no larger than original formula F, so redundancy is checked using formulas at most as large as F.

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