Computing the transitive closure of a union of affine integer tuple relations

Anna Beletska (1) , Denis Barthou (2) , Wlodzirmierz Bielecki (3) , Albert Cohen (1)

1 ALCHEMY - Architectures, Languages and Compilers to Harness the End of Moore Years
2 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation
3 ZUT - West Pomeranian University of Technology in Szczecin

This paper proposes a method to compute the transitive clo- sure of a union of a±ne 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 ex- ist little but special cases and incomplete heuristics. We introduce a novel su±cient and necessary condition de¯ning a class of relations for which an exact computation is possible. Our method is immediately applica- ble to a wide area of symbolic computation problems. It is illustrated on representative examples and compared with state-of-the-art approaches.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]

Anna Beletska, Denis Barthou, Wlodzirmierz Bielecki, Albert Cohen. Computing the transitive closure of a union of affine integer tuple relations. Conference on Combinatorial Optimization and Applications, Jun 2009, Huangshan, China. p98-109. ⟨hal-00575959⟩