VPSPACE and a transfer theorem over the complex field
Computational Complexity
2007-06-12 v1
Abstract
We extend the transfer theorem of [KP2007] to the complex field. That is, we investigate the links between the class VPSPACE of families of polynomials and the Blum-Shub-Smale model of computation over C. Roughly speaking, a family of polynomials is in VPSPACE if its coefficients can be computed in polynomial space. Our main result is that if (uniform, constant-free) VPSPACE families can be evaluated efficiently then the class PAR of decision problems that can be solved in parallel polynomial time over the complex field collapses to P. As a result, one must first be able to show that there are VPSPACE families which are hard to evaluate in order to separate P from NP over C, or even from PAR.
Keywords
Cite
@article{arxiv.0706.1477,
title = {VPSPACE and a transfer theorem over the complex field},
author = {Pascal Koiran and Sylvain Perifel},
journal= {arXiv preprint arXiv:0706.1477},
year = {2007}
}