Polynomial Precise Interval Analysis Revisited

Abstract : We consider a class of arithmetic equations over the complete lattice of integers (extended with −∞ and ∞) and provide a polynomial time algorithm for computing least solutions. For systems of equations with addition and least upper bounds, this algorithm is a smooth generalization of the Bellman-Ford al- gorithm for computing the single source shortest path in presence of positive and negative edge weights. The method then is extended to deal with more general forms of operations as well as minima with constants. For the latter, a controlled widening is applied at loops where unbounded increase occurs. We apply this algorithm to construct a cubic time algorithm for the class of interval equations using least upper bounds, addition, intersection with constant intervals as well as multiplication.
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Thomas Gawlitza, Jérôme Leroux, Jan Reineke, Helmut Seidl, Grégoire Sutre, et al.. Polynomial Precise Interval Analysis Revisited. Essays Dedicated to Kurt Mehlhorn on the Occasion of His 60th Birthday, Aug 2009, Saarbrücken, Germany. pp.422-437, ⟨10.1007/978-3-642-03456-5_28⟩. ⟨hal-00414750⟩

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