English

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

R2 v1 2026-07-22T12:21:16.264Z