%0 Journal Article
%T Two- versus three-dimensional connectivity testing of first-order queries to semi-algebraic sets
%A Floris Geerts
%A Lieven Smits
%A Jan Van den Bussche
%J Computer Science
%D 2003
%I arXiv
%R 10.1007/s00236-005-0171-5
%X This paper addresses the question whether one can determine the connectivity of a semi-algebraic set in three dimensions by testing the connectivity of a finite number of two-dimensional ``samples'' of the set, where these samples are defined by first-order queries. The question is answered negatively for two classes of first-order queries: cartesian-product-free, and positive one-pass.
%U http://arxiv.org/abs/cs/0308001v2