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sav07_lecture_9_skeleton [2007/04/17 15:14] vkuncak |
sav07_lecture_9_skeleton [2007/04/19 11:53] vkuncak |
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\end{equation*} | \end{equation*} | ||
where $a^1,\ldots,a^n$ are variables ranging over a lattice $A$ (one for each control-flow graph node), and $f_k$ are monotonic functions on $A$ (one for each edge in the control-flow graph). | where $a^1,\ldots,a^n$ are variables ranging over a lattice $A$ (one for each control-flow graph node), and $f_k$ are monotonic functions on $A$ (one for each edge in the control-flow graph). | ||
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==== From a system of equations to one equation ==== | ==== From a system of equations to one equation ==== | ||
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* [[http://www.di.ens.fr/~cousot/COUSOTpapers/POPL79.shtml|Systematic Design of Program Analysis Frameworks]] | * [[http://www.di.ens.fr/~cousot/COUSOTpapers/POPL79.shtml|Systematic Design of Program Analysis Frameworks]] | ||
+ | === Widening === | ||
+ | === Narrowing === | ||
- | ===== ASTREE Static Analyzer ===== | + | === Reduced product === |
- | + | ||
- | === A Static Analyzer for Large Safety-Critical Software === | + | |
- | + | ||
- | [[http://www.di.ens.fr/~cousot/COUSOTpapers/PLDI03.shtml|Link to paper]] | + | |
- | + | ||
- | Section 5.4: A remark on notation: | + | |
- | * if $\rho$ denotes the state and $S$ is a deterministic statement, then $[\![S]\!]^s(\rho)$ represents the new state after executing the statement; the relation corresponding to statement semantics would be $\{(S,[\![S]\!]^s(\rho)) \mid \rho \mbox{ is a state, mapping variables to their values \}$. | + | |
- | * this function is extended to map sets of states to sets of states, which gives function ampping $E$ to $[\![S]\!]^c(E)$ and is what we called strongest postcondition $sp(S,E)$. | + | |
- | + | ||
- | === The Octagon Abstract Domain === | + | |
- | + | ||
- | [[http://www.di.ens.fr/~mine/publi/article-mine-HOSC06.pdf|Link to paper]] | + | |
- | + | ||
- | === Combination of Abstractions in the ASTRÉE Static Analyzer === | + | |
- | + | ||
- | * [[http://www.di.ens.fr/~cousot/COUSOTpapers/ASIAN06.shtml|Link to paper]] | + | |