Hunter, Paul ;
Bouyer, Patricia ;
Markey, Nicolas ;
Ouaknine, Joël ;
Worrell, James
Computing Rational Radical Sums in Uniform TC^0
Abstract
A fundamental problem in numerical computation and computational geometry is to determine the sign of arithmetic expressions in radicals. Here we consider the simpler problem of deciding whether $\sum_{i=1}^m C_i A_i^{X_i}$ is zero for given rational numbers $A_i$, $C_i$, $X_i$. It has been known for almost twenty years that this can be decided in polynomial time. In this paper we improve this result by showing membership in uniform TC0. This requires several significant departures from Blömer's polynomialtime algorithm as the latter crucially relies on primitives, such as gcd computation and binary search, that are not known to be in TC0.
BibTeX  Entry
@InProceedings{hunter_et_al:LIPIcs:2010:2873,
author = {Paul Hunter and Patricia Bouyer and Nicolas Markey and Jo{\"e}l Ouaknine and James Worrell},
title = {{Computing Rational Radical Sums in Uniform TC^0}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)},
pages = {308316},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897231},
ISSN = {18688969},
year = {2010},
volume = {8},
editor = {Kamal Lodaya and Meena Mahajan},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2010/2873},
URN = {urn:nbn:de:0030drops28739},
doi = {http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2010.308},
annote = {Keywords: Sum of square roots, Threshold circuits, Complexity}
}
2010
Keywords: 

Sum of square roots, Threshold circuits, Complexity 
Seminar: 

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)

Related Scholarly Article: 


Issue date: 

2010 
Date of publication: 

2010 