A Specific Quantifier Elimination for Inner Box Test in Distance Constraints with UncertaintiesReport as inadecuate




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1 COPRIN - Constraints solving, optimization and robust interval analysis CRISAM - Inria Sophia Antipolis - Méditerranée , ENPC - École des Ponts ParisTech

Abstract : This document presents a specific quantifier elimination algorithm for distance constraints with uncertainties represented by constraints with existentially quantified parameters. Generally, the solution set of this type of constraints has a non-null volume, and therefore an interval based solver that implements a branch and prune algorithm will bisect again and again the boxes included inside the solution set, leading to inefficient computation. This situation can be strongly improved using a test for detecting inner boxes. In this work, we show how interval arithmetics can be successfully used for building an inner box test in some types of constraints and how it can be combined with a quantifier elimination algorithm for handling constraints with existentially quantified parameters.

Mots-clés : INTERVAL ANALYSIS CONSTRAINT PROGRAMMING QUANTIFIER ELIMINATION UNCERTAINTY DISTANCE EQUATIONS





Author: Carlos Grandón - Bertrand Neveu -

Source: https://hal.archives-ouvertes.fr/



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