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| The fact that we only used conjunctions is our analysis makes it **path-insensitive**. Intuitively, since we're only taking conjunctions, our normalization is too conservative and we will not be able to retain properties associated to certain paths. **Path-sensitivity** is often used as a measure of the precision of an analysis. | The fact that we only used conjunctions is our analysis makes it **path-insensitive**. Intuitively, since we're only taking conjunctions, our normalization is too conservative and we will not be able to retain properties associated to certain paths. **Path-sensitivity** is often used as a measure of the precision of an analysis. | ||
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| (an example of Dependent Attribute Analysis) | (an example of Dependent Attribute Analysis) | ||
| - | As we just saw, our analysis domain turned out to be too restricted. We may want to use a more extended one. Let's define a new set of formulas: | + | As we just saw, our analysis domain turned out to be too restrictive. We may want to use a more extended one. Let's define a new set of formulas: |
| $A^+ = \{ \bigvee (P_{i1} \wedge ... \wedge P_{in}) | P_{ij} \in \{Q_1, ..., Q_n\}) \}$ | $A^+ = \{ \bigvee (P_{i1} \wedge ... \wedge P_{in}) | P_{ij} \in \{Q_1, ..., Q_n\}) \}$ | ||
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| * [[predicate abstraction]] (Cartesian abstraction) | * [[predicate abstraction]] (Cartesian abstraction) | ||
| * [[http://research.microsoft.com/esp/pubs/esp-dataflow.pdf|ESP paper]] | * [[http://research.microsoft.com/esp/pubs/esp-dataflow.pdf|ESP paper]] | ||
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| ==== Linear inequalities ==== | ==== Linear inequalities ==== | ||
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| + | (section not covered in class) | ||
| Example implementation: [[http://www.cs.unipr.it/ppl/|Parma Polyhedra Library]] and a [[http://www.cs.unipr.it/ppl/Documentation/BagnaraHZ06TR.pdf|paper about Parma]]. Geometric interpretation of linear equations. | Example implementation: [[http://www.cs.unipr.it/ppl/|Parma Polyhedra Library]] and a [[http://www.cs.unipr.it/ppl/Documentation/BagnaraHZ06TR.pdf|paper about Parma]]. Geometric interpretation of linear equations. | ||