Topological lower bounds for arithmetic networks
Computational Complexity
2016-07-14 v3 Algebraic Geometry
Abstract
We prove a complexity lower bound on deciding membership in a semialgebraic set for arithmetic networks in terms of the sum of Betti numbers with respect to "ordinary" (singular) homology. This result complements a similar lower bound by Montana, Morais and Pardo for locally close semialgebraic sets in terms of the sum of Borel-Moore Betti numbers. We also prove a lower bound in terms of the sum of Betti numbers of the projection of a semialgebraic set to a coordinate subspace.
Cite
@article{arxiv.1510.03387,
title = {Topological lower bounds for arithmetic networks},
author = {Andrei Gabrielov and Nicolai Vorobjov},
journal= {arXiv preprint arXiv:1510.03387},
year = {2016}
}
Comments
19 pages, 10 figures