Abstract
We introduce a new numerical abstract domain, so-called interval polyhedra (itvPol), to infer and propagate interval linear constraints over program variables. itvPol, which allows to represent constraints of the form ∑ k [a k ,b k ]x k ≤ c, is more expressive than the classic convex polyhedra domain and allows to express certain non-convex (even unconnected) properties. The implementation of itvPol can be constructed based on interval linear programming and an interval variant of Fourier-Motzkin elimination. The preliminary experimental results of our prototype are encouraging, especially for programs affected by interval uncertainty, e.g., due to uncertain input data or interval-based abstractions of disjunctive, non-linear, or floating-point expressions. To our knowledge, this is the first application of interval linear algebra to static analysis.
This work is supported by the INRIA project “Abstraction” common to CNRS and ENS in France, and by the National Natural Science Foundation of China under Grant No.60725206.
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Chen, L., Miné, A., Wang, J., Cousot, P. (2009). Interval Polyhedra: An Abstract Domain to Infer Interval Linear Relationships. In: Palsberg, J., Su, Z. (eds) Static Analysis. SAS 2009. Lecture Notes in Computer Science, vol 5673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03237-0_21
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