Simple and Efficient Algorithms for Octagons

The numerical domain of Octagons can be viewed as an exercise in simplicity: it trades expressiveness for efficiency and ease of implementation. The domain can represent unary and dyadic constraints where the coefficients are +1 or -1, so called octagonal constraints, and comes with operations that have cubic complexity. The central operation is closure which computes a canonical form by deriving all implied octagonal constraints from a given octagonal system. This paper investigates the role of incrementality, namely closing a system where only one constraint has been changed, which is a dominating use-case. We present two new incremental algorithms for closure both of which are conceptually simple and computationally efficient, and argue their correctness