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 ∑i=1..m CiAiXi is zero for given rational numbers Ai, Ci, Xi. 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 polynomial-time algorithm as the latter crucially relies on primitives, such as gcd computation and binary search, that are not known to be in TC0.
Proceedings of FSTTCS 10, LIPICS 8, 2010. 9 pages.
© 2010 Patricia Bouyer, Paul Hunter, Nicolas Markey, Joël
Ouaknine, and James Worrell.