{"file":[{"file_size":844224,"relation":"main_file","file_id":"10634","creator":"cchlebak","file_name":"2021_LIPIcs_Arrighi.pdf","content_type":"application/pdf","success":1,"date_updated":"2022-01-17T10:49:03Z","date_created":"2022-01-17T10:49:03Z","access_level":"open_access","checksum":"d5a82ba893c3bc5da5914edbb3efb92b"}],"department":[{"_id":"KrCh"}],"publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","day":"29","article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","abstract":[{"text":"In the Intersection Non-emptiness problem, we are given a list of finite automata A_1, A_2,… , A_m over a common alphabet Σ as input, and the goal is to determine whether some string w ∈ Σ^* lies in the intersection of the languages accepted by the automata in the list. We analyze the complexity of the Intersection Non-emptiness problem under the promise that all input automata accept a language in some level of the dot-depth hierarchy, or some level of the Straubing-Thérien hierarchy. Automata accepting languages from the lowest levels of these hierarchies arise naturally in the context of model checking. We identify a dichotomy in the dot-depth hierarchy by showing that the problem is already NP-complete when all input automata accept languages of the levels B_0 or B_{1/2} and already PSPACE-hard when all automata accept a language from the level B_1. Conversely, we identify a tetrachotomy in the Straubing-Thérien hierarchy. More precisely, we show that the problem is in AC^0 when restricted to level L_0; complete for L or NL, depending on the input representation, when restricted to languages in the level L_{1/2}; NP-complete when the input is given as DFAs accepting a language in L_1 or L_{3/2}; and finally, PSPACE-complete when the input automata accept languages in level L_2 or higher. Moreover, we show that the proof technique used to show containment in NP for DFAs accepting languages in L_1 or L_{3/2} does not generalize to the context of NFAs. To prove this, we identify a family of languages that provide an exponential separation between the state complexity of general NFAs and that of partially ordered NFAs. To the best of our knowledge, this is the first superpolynomial separation between these two models of computation.","lang":"eng"}],"volume":213,"file_date_updated":"2022-01-17T10:49:03Z","date_created":"2022-01-16T23:01:29Z","publication":"41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science","language":[{"iso":"eng"}],"publication_status":"published","_id":"10630","scopus_import":"1","oa":1,"date_published":"2021-11-29T00:00:00Z","citation":{"ama":"Arrighi E, Fernau H, Hoffmann S, et al. On the complexity of intersection non-emptiness for star-free language classes. In: <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>. Vol 213. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34\">10.4230/LIPIcs.FSTTCS.2021.34</a>","ieee":"E. Arrighi <i>et al.</i>, “On the complexity of intersection non-emptiness for star-free language classes,” in <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Virtual, 2021, vol. 213.","mla":"Arrighi, Emmanuel, et al. “On the Complexity of Intersection Non-Emptiness for Star-Free Language Classes.” <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, vol. 213, 34, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34\">10.4230/LIPIcs.FSTTCS.2021.34</a>.","short":"E. Arrighi, H. Fernau, S. Hoffmann, M. Holzer, I.R. Jecker, M. De Oliveira Oliveira, P. Wolf, in:, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","apa":"Arrighi, E., Fernau, H., Hoffmann, S., Holzer, M., Jecker, I. R., De Oliveira Oliveira, M., &#38; Wolf, P. (2021). On the complexity of intersection non-emptiness for star-free language classes. In <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i> (Vol. 213). Virtual: Schloss Dagstuhl - Leibniz Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34\">https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34</a>","ista":"Arrighi E, Fernau H, Hoffmann S, Holzer M, Jecker IR, De Oliveira Oliveira M, Wolf P. 2021. On the complexity of intersection non-emptiness for star-free language classes. 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. FSTTCS: Foundations of Software Technology and Theoretical Computer Science, LIPIcs, vol. 213, 34.","chicago":"Arrighi, Emmanuel, Henning Fernau, Stefan Hoffmann, Markus Holzer, Ismael R Jecker, Mateus De Oliveira Oliveira, and Petra Wolf. “On the Complexity of Intersection Non-Emptiness for Star-Free Language Classes.” In <i>41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science</i>, Vol. 213. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34\">https://doi.org/10.4230/LIPIcs.FSTTCS.2021.34</a>."},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"intvolume":"       213","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"title":"On the complexity of intersection non-emptiness for star-free language classes","quality_controlled":"1","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-9597-7215-0"]},"year":"2021","ec_funded":1,"month":"11","date_updated":"2022-01-17T10:56:19Z","oa_version":"Published Version","alternative_title":["LIPIcs"],"conference":{"start_date":"2021-12-15","location":"Virtual","name":"FSTTCS: Foundations of Software Technology and Theoretical Computer Science","end_date":"2021-12-17"},"author":[{"first_name":"Emmanuel","last_name":"Arrighi","full_name":"Arrighi, Emmanuel"},{"full_name":"Fernau, Henning","last_name":"Fernau","first_name":"Henning"},{"full_name":"Hoffmann, Stefan","last_name":"Hoffmann","first_name":"Stefan"},{"last_name":"Holzer","first_name":"Markus","full_name":"Holzer, Markus"},{"full_name":"Jecker, Ismael R","id":"85D7C63E-7D5D-11E9-9C0F-98C4E5697425","first_name":"Ismael R","last_name":"Jecker"},{"last_name":"De Oliveira Oliveira","first_name":"Mateus","full_name":"De Oliveira Oliveira, Mateus"},{"full_name":"Wolf, Petra","first_name":"Petra","last_name":"Wolf"}],"status":"public","external_id":{"arxiv":["2110.01279"]},"acknowledgement":"We like to thank Lukas Fleischer and Michael Wehar for our discussions. This work started at the Schloss Dagstuhl Event 20483 Moderne Aspekte der Komplexitätstheorie in der Automatentheorie https://www.dagstuhl.de/20483.\r\n","article_number":"34","ddc":["000"],"has_accepted_license":"1","type":"conference","doi":"10.4230/LIPIcs.FSTTCS.2021.34"}