Precise sequential and parallel complexity bounds for quantifier elimination over algebraically closed fields

https://doi.org/10.1016/0022-4049(90)90159-FGet rights and content
Under an Elsevier user license
open archive

Abstract

This paper deals mainly with fast quantifier elimination in the elementary theory of algebraically closed fields of any characteristic. It is subdivided into an introduction, a short exposition of the computational model and of our results, and concludes with a section dedicated to proofs.

The new outcomes concern parallelism where the number of processors is controlled by the intrinsic sequential complexity of quantifier elimination. Our algorithms are optimal from the point of view of the overall complexities in parallel and in sequential (number of processors).

Due to recent progress concerning Triviality Testing of Polynomial Ideals (relying on effective affine Nullstellensätze) we are able to give upper bounds in a refined and satisfactory precise form.

Cited by (0)

A preliminary version of this paper (A. Galligo, J. Heintz and J. Morgenstern: Parallelism and fast quantifier elimination over algebraically (and real) closed fields) has been presented at “Fundamentals of Computation Theory” (FCT'87), Kazan, USSR, 1987.