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Section: New Results

An Abstract Domain to Infer Interval Linear Relationships

Participants : Liqian Chen, Antoine Miné, Ji Wang [ National Laboratory for Parallel and Distributed Processing, Changsha, P. R. China ] , Patrick Cousot.

In previous work [75] , we proposed a sound floating-point version of the polyhedron abstract domain. Soundness was achieved despite rounding errors by leveraging previous works on rigorous linear programming and designing a version of Fourier–Motzkin elimination using interval arithmetics internally.

In [21] , we propose an alternate construction where intervals appear explicitly in the abstract representation. Hence, the domain, so called interval polyhedra , can represent conjunctions of constraints of the form $ \upper_sigma$k[ak;bk]xk$ \le$c . Thus, we avoid the loss of precision that occurred in our previous work when converting the interval constraints that appeared naturally into scalar ones at the end of each operation. An added benefit is that this domain is strictly more expressive than regular polyhedra, as it can express some non-convex and even unconnected sets. The operations are based on interval linear programming and an interval variant of Fourier–Motzkin elimination, and can be implemented soundly using only floating-point arithmetics, thus ensuring a good time and memory complexity (in particular, we are free of the issue of coefficient explosion occurring in classic implementations that employ arbitrary precision exact rationals). Our prototype implementation shows encouraging preliminary implementation results. In particular, it can prove some disjunctive and non-linear properties out of the scope of the classic polyhedra domain.


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