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sav07_lecture_13_skeleton [2007/05/02 09:57] vkuncak |
sav07_lecture_13_skeleton [2007/05/02 15:19] (current) vkuncak |
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| * model checking (finite state or pushdown system) | * model checking (finite state or pushdown system) | ||
| * counterexample-driven refinement | * counterexample-driven refinement | ||
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| + | Today: abstraction | ||
| ==== Abstraction ==== | ==== Abstraction ==== | ||
| + | |||
| + | Main readings: | ||
| + | * [[http://www-verimag.imag.fr/~graf/biblio.php?view=full#GrafSaidi97|Construction of abstract state graphs with PVS]] | ||
| + | * [[http://www.mpi-sb.mpg.de/~podelski/papers/cartesian.ps|Boolean and Cartesian Abstraction for Model Checking C Programs, Thomas Ball, Andreas Podelski, Sriram K. Rajamani. TACAS 2001: 268-283 (paper in .PS format)]] | ||
| + | * [[http://doi.acm.org/10.1145/378795.378846|Automatic Predicate Abstraction of C Programs, Thomas Ball, Rupak Majumdar, Todd D. Millstein, Sriram K. Rajamani. PLDI 2001: 203-213]] | ||
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| Design space of abstractions: | Design space of abstractions: | ||
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| * focus (splitting, case analysis) | * focus (splitting, case analysis) | ||
| * best transformer in abstract domain | * best transformer in abstract domain | ||
| + | |||
| + | Examples. | ||
| + | |||
| + | Computation using wp. Weakest predicate abstraction of a given formula. Boolean programs. | ||
| + | |||
| + | Precision-preserving optimizations: | ||
| + | * cubes in increasing order | ||
| + | * do not update variables if command cannot change them | ||
| + | * cone of influence to reduce the number of predicates to consider | ||
| + | * syntactic construction of predicates | ||
| + | * caching of calls to theorem prover | ||
| + | Approximations: | ||
| + | * bounding cube length to 3 | ||
| + | * distributing approximation through logical operations | ||