{"day":"01","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ec_funded":1,"publisher":"Schloss Dagstuhl- Leibniz-Zentrum fur Informatik","year":"2016","date_published":"2016-08-01T00:00:00Z","title":"On the skolem problem for continuous linear dynamical systems","scopus_import":1,"quality_controlled":"1","oa_version":"Published Version","publist_id":"6314","language":[{"iso":"eng"}],"intvolume":"        55","pubrep_id":"778","file":[{"file_size":521415,"content_type":"application/pdf","date_updated":"2018-12-12T10:16:26Z","file_id":"5213","creator":"system","date_created":"2018-12-12T10:16:26Z","relation":"main_file","file_name":"IST-2017-778-v1+1_LIPIcs-ICALP-2016-100.pdf","access_level":"open_access"}],"status":"public","project":[{"call_identifier":"FWF","name":"Rigorous Systems Engineering","_id":"25832EC2-B435-11E9-9278-68D0E5697425","grant_number":"S 11407_N23"},{"grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","name":"Quantitative Graph Games: Theory and Applications","call_identifier":"FP7"},{"grant_number":"267989","_id":"25EE3708-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Quantitative Reactive Modeling"}],"file_date_updated":"2018-12-12T10:16:26Z","oa":1,"ddc":["004","006"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"KrCh"}],"acknowledgement":"Ventsislav Chonev is supported by Austrian Science Fund (FWF) NFN Grant No S11407-N23 (RiSE/SHiNE), ERC Start grant (279307:  Graph Games), and ERC Advanced Grant (267989: QUAREM).","date_created":"2018-12-11T11:49:59Z","month":"08","citation":{"chicago":"Chonev, Ventsislav K, Joël Ouaknine, and James Worrell. “On the Skolem Problem for Continuous Linear Dynamical Systems,” Vol. 55. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2016.100\">https://doi.org/10.4230/LIPIcs.ICALP.2016.100</a>.","ista":"Chonev VK, Ouaknine J, Worrell J. 2016. On the skolem problem for continuous linear dynamical systems. ICALP: Automata, Languages and Programming, LIPIcs, vol. 55, 100.","apa":"Chonev, V. K., Ouaknine, J., &#38; Worrell, J. (2016). On the skolem problem for continuous linear dynamical systems (Vol. 55). Presented at the ICALP: Automata, Languages and Programming, Rome, Italy: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2016.100\">https://doi.org/10.4230/LIPIcs.ICALP.2016.100</a>","short":"V.K. Chonev, J. Ouaknine, J. Worrell, in:, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016.","mla":"Chonev, Ventsislav K., et al. <i>On the Skolem Problem for Continuous Linear Dynamical Systems</i>. Vol. 55, 100, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik, 2016, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2016.100\">10.4230/LIPIcs.ICALP.2016.100</a>.","ama":"Chonev VK, Ouaknine J, Worrell J. On the skolem problem for continuous linear dynamical systems. In: Vol 55. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik; 2016. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2016.100\">10.4230/LIPIcs.ICALP.2016.100</a>","ieee":"V. K. Chonev, J. Ouaknine, and J. Worrell, “On the skolem problem for continuous linear dynamical systems,” presented at the ICALP: Automata, Languages and Programming, Rome, Italy, 2016, vol. 55."},"alternative_title":["LIPIcs"],"conference":{"name":"ICALP: Automata, Languages and Programming","location":"Rome, Italy","start_date":"2016-07-12","end_date":"2016-07-15"},"doi":"10.4230/LIPIcs.ICALP.2016.100","author":[{"full_name":"Chonev, Ventsislav K","first_name":"Ventsislav K","id":"36CBE2E6-F248-11E8-B48F-1D18A9856A87","last_name":"Chonev"},{"full_name":"Ouaknine, Joël","first_name":"Joël","last_name":"Ouaknine"},{"first_name":"James","full_name":"Worrell, James","last_name":"Worrell"}],"_id":"1069","article_number":"100","abstract":[{"lang":"eng","text":"The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differen-\r\ntial equation has a zero in a given interval of real numbers. This is a fundamental reachability\r\nproblem for continuous linear dynamical systems, such as linear hybrid automata and continuous-\r\ntime Markov chains. Decidability of the problem is currently open – indeed decidability is open\r\neven for the sub-problem in which a zero is sought in a bounded interval. In this paper we show\r\ndecidability of the bounded problem subject to Schanuel’s Conjecture, a unifying conjecture in\r\ntranscendental number theory. We furthermore analyse the unbounded problem in terms of the\r\nfrequencies of the differential equation, that is, the imaginary parts of the characteristic roots.\r\nWe show that the unbounded problem can be reduced to the bounded problem if there is at most\r\none rationally linearly independent frequency, or if there are two rationally linearly independent\r\nfrequencies and all characteristic roots are simple. We complete the picture by showing that de-\r\ncidability of the unbounded problem in the case of two (or more) rationally linearly independent\r\nfrequencies would entail a major new effectiveness result in Diophantine approximation, namely\r\ncomputability of the Diophantine-approximation types of all real algebraic numbers."}],"publication_status":"published","type":"conference","has_accepted_license":"1","volume":55,"date_updated":"2021-01-12T06:48:03Z"}