A new interval arithmetic to generate the complementary of contractors

Pierre Filiol (1, 2) , Théotime Bollengier (1, 3) , Luc Jaulin (1, 2) , Jean-Christophe Le Lann (1, 3)

1 ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne
2 Lab-STICC_ROBEX - Equipe ROBotics for EXploration
3 Lab-STICC_ARCAD - Equipe Hardware ARchitectures and CAD tools

Contractor algebra is used to characterize a set defined as a composition of sets defined by inequalities. It mainly uses interval methods combined with constraint propagation. This algebra includes the classical operations we have for sets such as the intersection, the union and the inversion. Now, it does not include to complement operator. The reason for this is probably related to the interval arithmetic itself. In this paper, we show that it we change the arithmetic used for intervals adding a single flag, similar to not a number, we are able to include easily the complement in the algebra of contractors.

Mots clés: Intervals; Contractors

Domaines: Architectures Matérielles [cs.AR]; Analyse numérique [cs.NA]

Pierre Filiol, Théotime Bollengier, Luc Jaulin, Jean-Christophe Le Lann. A new interval arithmetic to generate the complementary of contractors. Summer Workshop on Interval Methods, Jul 2022, Hannover, Germany. ⟨hal-03859346v1⟩