The Abstract Domain of Parallelotopes

We propose a numerical abstract domain based on parallelotopes. A parallelotope is a polyhedron whose constraint matrix is squared and invertible. The domain of parallelotopes is a fully relational abstraction of the Cousot and Halbwachsʼ polyhedra abstract domain, and does not use templates. We equip the domain of parallelotopes with all the necessary operations for the analysis of imperative programs, and show optimality results for the abstract operators.