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sav07_lecture_6_skeleton [2007/03/30 19:57] vkuncak |
sav07_lecture_6_skeleton [2007/03/30 20:18] vkuncak |
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| S is infinite, instead of S, we use a representation of some approximation of S. Because we want to be sure to account for all possibilities (and not miss errors), we use overapproximation of S. | S is infinite, instead of S, we use a representation of some approximation of S. Because we want to be sure to account for all possibilities (and not miss errors), we use overapproximation of S. | ||
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| Line 220: | Line 221: | ||
| This is the most important condition for abstract interpretation. | This is the most important condition for abstract interpretation. | ||
| - | |||
| - | When equality holds, we have the "best abstract transformer" (the most precise one) for a given $\gamma$. | ||
| One way to find $sp\#$ it is to have $\alpha$ that goes the other way | One way to find $sp\#$ it is to have $\alpha$ that goes the other way | ||
| Line 241: | Line 240: | ||
| sp\#(a,r) = \alpha(sp(\gamma(a),r)) | sp\#(a,r) = \alpha(sp(\gamma(a),r)) | ||
| \end{equation*} | \end{equation*} | ||
| + | and we call this "the best transformer". | ||
| - | All else being same, the best transformer is better, because it gives as precise results as we can get with a given analysis domain. But sometimes it can be more expensive so we use a weaker one. | ||
| ==== Lattices ==== | ==== Lattices ==== | ||
| + | |||
| + | Recall notions of [[preorder]], [[partial order]], [[equivalence relation]]. | ||
| Partial order where each two element set has | Partial order where each two element set has | ||