@article{1380, 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 NPRP.}, author = {Chonev, Ventsislav K and Ouaknine, Joël and Worrell, James}, journal = {Journal of the ACM}, number = {3}, publisher = {ACM}, title = {{On the complexity of the orbit problem}}, doi = {10.1145/2857050}, volume = {63}, year = {2016}, }