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sav07_lecture_3 [2007/03/29 21:05] kremena.diatchka |
sav07_lecture_3 [2007/04/11 13:51] vkuncak |
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| Note: when proving our verification condition, instead of proving that semantics of relation implies error=false, it's same as proving that the formula for set sp(U,r) implies error=false, where U is the universal relation, or, in terms of formulas, computing the strongest postcondition of formula 'true'. | Note: when proving our verification condition, instead of proving that semantics of relation implies error=false, it's same as proving that the formula for set sp(U,r) implies error=false, where U is the universal relation, or, in terms of formulas, computing the strongest postcondition of formula 'true'. | ||
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| ==== Weakest preconditions ==== | ==== Weakest preconditions ==== | ||
| While symbolic execution computes formula by going forward along the program syntax tree, [[sav07_lecture_2#weakest_preconditions|weakest precondition]] computes formula by going backward. | While symbolic execution computes formula by going forward along the program syntax tree, [[sav07_lecture_2#weakest_preconditions|weakest precondition]] computes formula by going backward. | ||
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| + | \begin{equation*} | ||
| + | wp(r,P) = \{ s_1 \mid \forall s_2. (s_1,s_2) \in r \rightarrow s_2 \in P \} | ||
| + | \end{equation*} | ||
| + | |||
| We know that the weakest precondition holds following conditions for each relation r and sets Q1, Q2: | We know that the weakest precondition holds following conditions for each relation r and sets Q1, Q2: | ||
| wp(r, Q1 ∧ Q2) = wp(r,Q1) ∧ wp(r,Q2) | wp(r, Q1 ∧ Q2) = wp(r,Q1) ∧ wp(r,Q2) | ||
| Line 203: | Line 209: | ||
| Proof: small model theorem. | Proof: small model theorem. | ||
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| * [[http://www.cs.nyu.edu/acsys/cvc3/download.html|CVC3]] (successor of CVC Lite) | * [[http://www.cs.nyu.edu/acsys/cvc3/download.html|CVC3]] (successor of CVC Lite) | ||
| * [[http://combination.cs.uiowa.edu/smtlib/|SMT-LIB]] Standard for formulas, competition | * [[http://combination.cs.uiowa.edu/smtlib/|SMT-LIB]] Standard for formulas, competition | ||
| + | * [[http://doi.acm.org/10.1145/135226.135233|Omega test]] conjunctions of integer inequalities | ||
| ==== Full Presburger arithmetic ==== | ==== Full Presburger arithmetic ==== | ||