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On the Complexity of the Orbit Problem
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}