Skip to Main content Skip to Navigation
Conference papers

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
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, CNRS - Centre National de la Recherche Scientifique : UMR8623, Inria Saclay - Ile de France
Abstract : 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.
Complete list of metadata

Cited literature [11 references]  Display  Hide  Download
Contributor : Denis Barthou Connect in order to contact the contributor
Submitted on : Friday, March 11, 2011 - 3:18:07 PM
Last modification on : Thursday, January 20, 2022 - 5:33:20 PM
Long-term archiving on: : Sunday, June 12, 2011 - 2:47:58 AM


Files produced by the author(s)


  • HAL Id : hal-00575959, version 1



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⟩



Les métriques sont temporairement indisponibles