Computing the Transitive Closure of a Union of Affine Integer Tuple Relations

Abstract. This paper proposes a method to compute the transitive closure of a union of affine relations on integer tuples. Within Presburger arithmetics, complete algorithms to compute the transitive closure exist for convex polyhedra only. In presence of non-convex relations, there exist little but special cases and incomplete heuristics. We introduce a novel sufficient and necessary condition defining a class of relations for which an exact computation is possible. Our method is immediately applicable to a wide area of symbolic computation problems. It is illustrated on representative examples and compared with state-of-the-art approaches.

• Type: Conference
• Year: 2009
• Where: COCOA
• Authors: Anna Beletska, Denis Barthou, Wlodzimierz Bielecki, Albert Cohen
• Keywords: Affine Relations, COCOA 2009, Discrete Geometry, Transitive Closure, Transitive Closure Exist