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

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

The Full Algorithm /* *

The Full Algorithm /* * Recursive algorithm to compute simplified form. * N: current subformula, C: critical constraint of N. */ simplify(N, C) { ­ If N is a leaf: } ­ If C => N return true /* Non­constraining */ ­ If C=> ¬N return false /* Non­relaxing */ ­ Otherwise, return N /* Neither */ ­ If N is a connective, for each child X of N: Critical constraint is recomputed because ­ Compute critical constraint C(X) siblings may change. ­ X = simplify(X, C(X)) ­ Repeat until no child of N can be further simplified.

Making it Practical 2n 2 ● Worst case: Requires validity checks. (n = # leaves) ● Important Optimization: – Insight: The leaves of the formulas whose validity is checked are always the same. – For simplifying SMT formulas, we can gainfully reuse the same conflict clauses throughout simplification ● Empirical Result: Overhead of simplification over solving sub­linear (logarithmic) in practice for constraints generated by our program analysis system.

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