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

Authors:
Anna Beletska;Denis Barthou;Wlodzimierz Bielecki;Albert Cohen
Affiliations:
INRIA Saclay, France;University of Versailles St. Quentin, France;Technical University of Szczecin, Poland;INRIA Saclay, France
Venue:
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Year:
2009

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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.