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 NPRP.
Proceedings of STOC 13, 2013. 9 pages.
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