… A key family of operations for the octagon domain are closure algorithms, which check … We
present new quadratic incremental algorithms for closure, strong closure and integer closure …

… Our contribution is to propose two new incremental algorithms for closing an octagon
represented as a DBM. These algorithms represent different points in the design space: the first is …

… extend the closure to coherent DBMs representing octagons. … 7 presents two closed DBMs
representing the same octagon … incremental algorithm is less powerful than our incremental …

… Here, we provide simplified cubic time algorithms for computing the closure of Octagon
abstract … The notion of 2-projectivity also lends itself to efficient algorithms for incremental …

… build abstract domains1 —such as the Octagon Abstract Domain implemented in the library
with … for strong closure. An incremental closure procedure for obtaining the tight closure of an …

… Cotton and Maler [16] show that a potential function π is particularly useful in incremental …
Loosely, for each abstract operationOp assumed to work on strongly closed graphs, we need to …

… Incremental Closure Minè introduced incremental closure [24] which reestablishes
closure once a small number of constraints are added to a closed DBM. This algorithm was …

… • A novel algorithm for computing incremental closure which brings down the number of
operations … • A novel sparse algorithm for incremental closure which exploits sparsity in matrices. …

… In fact, if we only update one (or a constant number of) constraint in the DBM, we can
recompute the tight closure in O(n2) using the incremental tight closure algorithm presented by …

… incremental closure on the octagon m. The argument m is supposed to be equal to a closed
octagon… It is modified in-place to recover the closure. O(N2) time cost and O(N) memory cost. …