Using interval arithmetic to prove that a set is path-connected

Authors:
Nicolas Delanoue;Luc Jaulin;Bertrand Cottenceau
Affiliations:
Laboratoire d'Ingénierie des Systèmes Automatisés, ISTIA, Angers, France;Laboratoire d'Ingénierie des Systèmes Automatisés, ISTIA, Angers, France;Laboratoire d'Ingénierie des Systèmes Automatisés, ISTIA, Angers, France
Venue:
Theoretical Computer Science - Real numbers and computers
Year:
2006

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Abstract

In this paper, we give a numerical algorithm able to prove whether a set S described by nonlinear inequalities is path-connected or not. To our knowledge, no other algorithm (numerical or symbolic) is able to deal with this type of problem. The proposed approach uses interval arithmetic to build a graph which has exactly the same number of connected components as S. Examples illustrate the principle of the approach.