16 research outputs found
Two- versus three-dimensional connectivity testing of first-order queries to semi-algebraic sets
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.Comment: corrected minor confusion in Proof of Theorem