The octagon abstract domain

The article presents a novel numerical abstract domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on Difference-Bound Matrices and allows us to represent invariants of the form (/spl plusmn/x/spl plusmn/y/spl les/c), where x and y are program variables and c is a real constant. We focus on giving an efficient representation based on Difference-Bound Matrices with O(n/sup 2/) memory cost, where n is the number of variables, and graph-based algorithms for all common abstract operators, with O(n/sup 3/) time cost. This includes a normal form algorithm to test the equivalence of representation and a widening operator to compute least fixpoint approximations.