Interval Polyhedra: An Abstract Domain to Infer Interval Linear Relationships

Authors:
Liqian Chen;Antoine Miné;Ji Wang;Patrick Cousot
Affiliations:
National Laboratory for Parallel and Distributed Processing, Changsha, P.R.China and École Normale Supérieure, Paris, France;École Normale Supérieure, Paris, France and CNRS, France;National Laboratory for Parallel and Distributed Processing, Changsha, P.R.China;École Normale Supérieure, Paris, France and CIMS, New York University, New York, NY, USA
Venue:
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Year:
2009

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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.