A measure of space for computing over the reals

Authors:
Paulin Jacobé de Naurois
Affiliations:
LIPN, Université Paris XIII, Villetaneuse, France
Venue:
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Year:
2006

Citing 5
Cited 1

PR≠NCR

Journal of Complexity
Two P-complete problems in the theory of the reals

Journal of Complexity
Separation of complexity classes in Koiran's weak model

Selected papers of the workshop on Continuous algorithms and complexity
A weak version of the Blum, Shub, and Smale model

Journal of Computer and System Sciences - Special issue: dedicated to the memory of Paris Kanellakis
Complexity and real computation

Complexity and real computation

Small-space analogues of Valiant's classes

FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose a new complexity measure of space for the BSS model of computation. We define LOGSPACEW and PSPACEW complexity classes over the reals. We prove that LOGSPACEW is included in ${\sf NC}^2_{\mathbb{R}} \cap {\sf P}_W$, i.e. is small enough for being relevant. We prove that the Real Circuit Decision Problem is Pℝ-complete under LOGSPACEW reductions, i.e. that LOGSPACEW is large enough for containing natural algorithms. We also prove that PSPACEW is included in PARℝ.