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

Simplified Form ● A **for**mula F is in simplified **for**m if no leaf in F is redundant. Important Fact: If a **for**mula is in simplified **for**m, we cannot obtain a smaller, equivalent **for**mula 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 **for**mula in simplified **for**m is satisfiable if and only if it is not syntactically false, and it is valid iff it is syntactically true. ● Simplified **for**ms are preserved under negation. ● Simplified **for**ms are not unique. ● Consider **for**mula in **line**ar integer arithmetic. Both and are simplified **for**ms. Equivalence of simplified **for**ms cannot be determined syntactically.

- Page 1 and 2: Small Formulas for Large Programs:
- Page 3 and 4: Techniques to Limit Formula Size
- Page 5 and 6: Goal #1: Non-redundancy ● Given f
- Page 7 and 8: An Example enum op_type {ADD=0, SUB
- Page 9 and 10: An Example enum op_type {ADD=0, SUB
- Page 11 and 12: Now that this example has convinced
- Page 13: Redundant Leaves ● A leaf L is no
- Page 17 and 18: Critical Constraint Idea: Compute a
- Page 19 and 20: Example ● Consider again the form
- Page 21 and 22: Example ● Consider again the form
- Page 23 and 24: Making it Practical 2n 2 ● Worst
- Page 25 and 26: Impact on Analysis Scalability Anal
- Page 27 and 28: It's not just Compass ● Measured
- Page 29: Any questions?