{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"has_accepted_license":"1","abstract":[{"text":"Quantitative automata are nondeterministic finite automata with edge weights. They value a\r\nrun by some function from the sequence of visited weights to the reals, and value a word by its\r\nminimal/maximal run. They generalize boolean automata, and have gained much attention in\r\nrecent years. Unfortunately, important automaton classes, such as sum, discounted-sum, and\r\nlimit-average automata, cannot be determinized. Yet, the quantitative setting provides the potential\r\nof approximate determinization. We define approximate determinization with respect to\r\na distance function, and investigate this potential.\r\nWe show that sum automata cannot be determinized approximately with respect to any\r\ndistance function. However, restricting to nonnegative weights allows for approximate determinization\r\nwith respect to some distance functions.\r\nDiscounted-sum automata allow for approximate determinization, as the influence of a word’s\r\nsuffix is decaying. However, the naive approach, of unfolding the automaton computations up\r\nto a sufficient level, is shown to be doubly exponential in the discount factor. We provide an\r\nalternative construction that is singly exponential in the discount factor, in the precision, and\r\nin the number of states. We prove matching lower bounds, showing exponential dependency on\r\neach of these three parameters.\r\nAverage and limit-average automata are shown to prohibit approximate determinization with\r\nrespect to any distance function, and this is the case even for two weights, 0 and 1.","lang":"eng"}],"type":"conference","alternative_title":["LIPIcs"],"file_date_updated":"2020-07-14T12:45:52Z","author":[{"last_name":"Boker","full_name":"Boker, Udi","first_name":"Udi","id":"31E297B6-F248-11E8-B48F-1D18A9856A87"},{"id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","full_name":"Henzinger, Thomas A","orcid":"0000−0002−2985−7724","last_name":"Henzinger"}],"date_published":"2012-12-01T00:00:00Z","scopus_import":1,"publication":"Leibniz International Proceedings in Informatics","conference":{"end_date":"2012-12-17","location":"Hyderabad, India","name":"FSTTCS: Foundations of Software Technology and Theoretical Computer Science","start_date":"2012-12-15"},"doi":"10.4230/LIPIcs.FSTTCS.2012.362","quality_controlled":"1","_id":"2891","department":[{"_id":"ToHe"}],"pubrep_id":"805","oa":1,"publication_status":"published","date_created":"2018-12-11T12:00:10Z","file":[{"creator":"system","content_type":"application/pdf","file_name":"IST-2017-805-v1+1_34.pdf","date_updated":"2020-07-14T12:45:52Z","access_level":"open_access","date_created":"2018-12-12T10:10:37Z","file_size":559069,"relation":"main_file","checksum":"88da18d3e2cb2e5011d7d10ce38a3864","file_id":"4826"}],"date_updated":"2020-08-11T10:09:52Z","language":[{"iso":"eng"}],"ddc":["004"],"page":"362 - 373","title":"Approximate determinization of quantitative automata","publist_id":"3867","year":"2012","volume":18,"project":[{"_id":"25832EC2-B435-11E9-9278-68D0E5697425","name":"Rigorous Systems Engineering","call_identifier":"FWF","grant_number":"S 11407_N23"},{"grant_number":"267989","name":"Quantitative Reactive Modeling","call_identifier":"FP7","_id":"25EE3708-B435-11E9-9278-68D0E5697425"}],"citation":{"chicago":"Boker, Udi, and Thomas A Henzinger. “Approximate Determinization of Quantitative Automata.” In Leibniz International Proceedings in Informatics, 18:362–73. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012. https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362.","ama":"Boker U, Henzinger TA. Approximate determinization of quantitative automata. In: Leibniz International Proceedings in Informatics. Vol 18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2012:362-373. doi:10.4230/LIPIcs.FSTTCS.2012.362","mla":"Boker, Udi, and Thomas A. Henzinger. “Approximate Determinization of Quantitative Automata.” Leibniz International Proceedings in Informatics, vol. 18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 362–73, doi:10.4230/LIPIcs.FSTTCS.2012.362.","ista":"Boker U, Henzinger TA. 2012. Approximate determinization of quantitative automata. Leibniz International Proceedings in Informatics. FSTTCS: Foundations of Software Technology and Theoretical Computer Science, LIPIcs, vol. 18. 362–373.","short":"U. Boker, T.A. Henzinger, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2012, pp. 362–373.","apa":"Boker, U., & Henzinger, T. A. (2012). Approximate determinization of quantitative automata. In Leibniz International Proceedings in Informatics (Vol. 18, pp. 362–373). Hyderabad, India: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.FSTTCS.2012.362","ieee":"U. Boker and T. A. Henzinger, “Approximate determinization of quantitative automata,” in Leibniz International Proceedings in Informatics, Hyderabad, India, 2012, vol. 18, pp. 362–373."},"day":"01","acknowledgement":"We thank Laurent Doyen for great ideas and valuable help in analyzing discounted-sum automata.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","ec_funded":1,"intvolume":" 18","status":"public","oa_version":"Published Version","month":"12"}