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sav08:forward_symbolic_execution [2009/03/10 22:54] vkuncak |
sav08:forward_symbolic_execution [2009/03/11 10:47] vkuncak |
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Then we continue only from this one state. | Then we continue only from this one state. | ||
+ | ===== Execution ===== | ||
- | ===== Underapproximations ===== | + | If the first statements are |
+ | assume (x=0) | ||
+ | assume (x=1) | ||
+ | Then symbolic execution knows the exact values and can work as an interpreter. | ||
- | We next consider testing and debugging applications. | ||
- | These can generate real counterexamples (underapproximation) as opposed to providing proofs (overapproximations). | + | ===== Underapproximations ===== |
+ | |||
+ | Here we generate real counterexamples (underapproximation), we compute smaller relation than one given by program semantics. | ||
If there are no loop invariants, we can still execute program on concrete inputs. For symbolic initial state (e.g. giving upper bound of loop) execution need not terminate. | If there are no loop invariants, we can still execute program on concrete inputs. For symbolic initial state (e.g. giving upper bound of loop) execution need not terminate. | ||
- | * Bounding depth: stop executing for path | + | * Bounding depth: stop executing for paths longer than some value |
* Bounding state: small integer width, small number of objects in heap | * Bounding state: small integer width, small number of objects in heap | ||
- | * Loop unrolling: replace loop( c ) with c;c;c for some number of times | + | * Loop unrolling: replace loop( c ) with c[]c;c[]c;c;c for some number of times |
* Instantiating values: find a satisfying assignment for R, take value v of x in it and replace e_x with v (moves towards concrete execution) | * Instantiating values: find a satisfying assignment for R, take value v of x in it and replace e_x with v (moves towards concrete execution) | ||
+ | |||
+ | |||
+ | ===== Overaproximation ===== | ||
+ | |||
+ | In this case we compute overaproximation, bigger relation than the actual relation given by program semantics. | ||
+ | |||
+ | Examples: | ||
+ | * do not maintain exact expressions for variables, but only whether they are positive | ||
+ | * maintain only linear or certain polynomial constraints - if actual constraints are more complex, keep only the polynomial constraints that are guaranteed to hold | ||
+ | |||
+ | Why we approximate we can obtain | ||
+ | * termination even for programs that have loops | ||
+ | * useful information about the program (not exactly all information that we are interested in, depends on the approximation) | ||
===== References ===== | ===== References ===== |