{"quality_controlled":"1","scopus_import":1,"title":"On the complexity of the orbit problem","_id":"1380","main_file_link":[{"url":"http://arxiv.org/abs/1303.2981","open_access":"1"}],"author":[{"first_name":"Ventsislav K","full_name":"Chonev, Ventsislav K","last_name":"Chonev","id":"36CBE2E6-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Ouaknine","first_name":"Joël","full_name":"Ouaknine, Joël"},{"first_name":"James","full_name":"Worrell, James","last_name":"Worrell"}],"doi":"10.1145/2857050","abstract":[{"text":"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.","lang":"eng"}],"article_number":"23","oa_version":"Preprint","issue":"3","publication_status":"published","publication":"Journal of the ACM","type":"journal_article","publist_id":"5831","date_updated":"2021-01-12T06:50:17Z","volume":63,"language":[{"iso":"eng"}],"intvolume":"        63","day":"01","status":"public","year":"2016","publisher":"ACM","oa":1,"date_published":"2016-06-01T00:00:00Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"KrCh"}],"month":"06","date_created":"2018-12-11T11:51:41Z","citation":{"ieee":"V. K. Chonev, J. Ouaknine, and J. Worrell, “On the complexity of the orbit problem,” <i>Journal of the ACM</i>, vol. 63, no. 3. ACM, 2016.","short":"V.K. Chonev, J. Ouaknine, J. Worrell, Journal of the ACM 63 (2016).","mla":"Chonev, Ventsislav K., et al. “On the Complexity of the Orbit Problem.” <i>Journal of the ACM</i>, vol. 63, no. 3, 23, ACM, 2016, doi:<a href=\"https://doi.org/10.1145/2857050\">10.1145/2857050</a>.","ama":"Chonev VK, Ouaknine J, Worrell J. On the complexity of the orbit problem. <i>Journal of the ACM</i>. 2016;63(3). doi:<a href=\"https://doi.org/10.1145/2857050\">10.1145/2857050</a>","apa":"Chonev, V. K., Ouaknine, J., &#38; Worrell, J. (2016). On the complexity of the orbit problem. <i>Journal of the ACM</i>. ACM. <a href=\"https://doi.org/10.1145/2857050\">https://doi.org/10.1145/2857050</a>","chicago":"Chonev, Ventsislav K, Joël Ouaknine, and James Worrell. “On the Complexity of the Orbit Problem.” <i>Journal of the ACM</i>. ACM, 2016. <a href=\"https://doi.org/10.1145/2857050\">https://doi.org/10.1145/2857050</a>.","ista":"Chonev VK, Ouaknine J, Worrell J. 2016. On the complexity of the orbit problem. Journal of the ACM. 63(3), 23."}}