Two- versus three-dimensional connectivity testing of first-order queries to semi-algebraic sets
Logic in Computer Science
2007-05-23 v2 Computational Geometry
Databases
Abstract
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.
Cite
@article{arxiv.cs/0308001,
title = {Two- versus three-dimensional connectivity testing of first-order queries to semi-algebraic sets},
author = {Floris Geerts and Lieven Smits and Jan Van den Bussche},
journal= {arXiv preprint arXiv:cs/0308001},
year = {2007}
}
Comments
corrected minor confusion in Proof of Theorem 1