On the Complexity of Numerical Analysis

We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis. We show that both hinge on the question of understanding the complexity of the following problem, which we call PosSLP: Given a divisionfree straight-line program producing an integer N, decide whether N > 0. We show that PosSLP lies in the counting hierarchy, and we show that if A is any language in the Boolean part of PR accepted by a machine whose machine constants are algebraic real numbers, then A PPosSLP . Combining our results with work of Tiwari, we show that the Euclidean Traveling Salesman Problem lies in the counting hierarchy

• Type: Conference
• Year: 2006
• Where: COCO
• Authors: Eric Allender, Peter Bürgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen
• Keywords: Algorithms, COCO 2006, Counting Hierarchy, Divisionfree Straight-line Program, Euclidean Traveling Salesman Problem