Transitive Closures of Affine Integer Tuple Relations and their Overapproximations
BibTeX
@MISC{Verdoolaege_transitiveclosures,
author = {Sven Verdoolaege and Albert Cohen and Anna Beletska and École Normale Supérieure},
title = {Transitive Closures of Affine Integer Tuple Relations and their Overapproximations},
year = {}
}
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Abstract
Computing the transitive closure of a relation is an operation underlying many important algorithms, with applications to computer-aided design, software engineering, scheduling, databases and optimizing compilers. In this paper, we consider the class of parametrized relations over integer tuples whose constraints consist of affine equalities and inequalities over variables, parameters and existentially quantified variables. This class has the same expressivity as Presburger arithmetic. Such quasi-affine relations typically describe infinite graphs, with the transitive closure corresponding to the set of all paths in the graph, and are widespread in decision and optimization problems with infinite domains, with applications to static analysis, formal verification and automatic
