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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.
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  • HAL Id : hal-00575959, version 1

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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⟩

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