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

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

## Simplified Form ● A

Simplified Form ● A formula F is in simplified form if no leaf in F is redundant. Important Fact: If a formula is in simplified form, we cannot obtain a smaller, equivalent formula by replacing any subset of the leaves by true or false. This means that we only need to check one leaf at a time for redundancy, not subsets of leaves.

Properties of Simplified Forms ● A formula in simplified form is satisfiable if and only if it is not syntactically false, and it is valid iff it is syntactically true. ● Simplified forms are preserved under negation. ● Simplified forms are not unique. ● Consider formula in linear integer arithmetic. Both and are simplified forms. Equivalence of simplified forms cannot be determined syntactically.

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