On the Complexity of the Orbit Problem
Computational Complexity
2016-06-23 v3 Data Structures and Algorithms
Abstract
We consider higher-dimensional versions of Kannan and Lipton's Orbit Problem---determining whether a target vector space V may be reached from a starting point x under repeated applications of a linear transformation A. Answering two questions posed by Kannan and Lipton in the 1980s, we show that when V has dimension one, this problem is solvable in polynomial time, and when V has dimension two or three, the problem is in NP^{RP}.
Keywords
Cite
@article{arxiv.1303.2981,
title = {On the Complexity of the Orbit Problem},
author = {Ventsislav Chonev and Joël Ouaknine and James Worrell},
journal= {arXiv preprint arXiv:1303.2981},
year = {2016}
}