{"abstract":[{"text":"Graphs and games on graphs are fundamental models for the analysis of reactive systems, in particular, for model-checking and the synthesis of reactive systems. The class of ω-regular languages provides a robust specification formalism for the desired properties of reactive systems. In the classical infinitary formulation of the liveness part of an ω-regular specification, a \"good\" event must happen eventually without any bound between the good events. A stronger notion of liveness is bounded liveness, which requires that good events happen within d transitions. Given a graph or a game graph with n vertices, m edges, and a bounded liveness objective, the previous best-known algorithmic bounds are as follows: (i) O(dm) for graphs, which in the worst-case is O(n³); and (ii) O(n² d²) for games on graphs. Our main contributions improve these long-standing algorithmic bounds. For graphs we present: (i) a randomized algorithm with one-sided error with running time O(n^{2.5} log n) for the bounded liveness objectives; and (ii) a deterministic linear-time algorithm for the complement of bounded liveness objectives. For games on graphs, we present an O(n² d) time algorithm for the bounded liveness objectives.","lang":"eng"}],"department":[{"_id":"KrCh"}],"date_published":"2021-07-02T00:00:00Z","publication_status":"published","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2022-08-12T10:55:02Z","article_processing_charge":"No","month":"07","day":"02","file":[{"date_created":"2021-10-01T08:49:26Z","file_size":854576,"success":1,"file_id":"10062","date_updated":"2021-10-01T08:49:26Z","access_level":"open_access","creator":"cchlebak","file_name":"2021_LIPIcs_Chatterjee.pdf","content_type":"application/pdf","checksum":"5a3fed8dbba8c088cbeac1e24cc10bc5","relation":"main_file"}],"type":"conference","alternative_title":["LIPIcs"],"status":"public","title":"Faster algorithms for bounded liveness in graphs and game graphs","quality_controlled":"1","scopus_import":"1","publisher":"Schloss Dagstuhl - Leibniz Zentrum für Informatik","date_created":"2021-09-27T14:33:15Z","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","oa":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"_id":"10054","article_number":"124","ec_funded":1,"conference":{"location":"Glasgow, Scotland","end_date":"2021-07-16","name":"ICALP: International Colloquium on Automata, Languages, and Programming","start_date":"2021-07-12"},"citation":{"ieee":"K. Chatterjee, M. H. Henzinger, S. S. Kale, and A. Svozil, “Faster algorithms for bounded liveness in graphs and game graphs,” in <i>48th International Colloquium on Automata, Languages, and Programming</i>, Glasgow, Scotland, 2021, vol. 198.","mla":"Chatterjee, Krishnendu, et al. “Faster Algorithms for Bounded Liveness in Graphs and Game Graphs.” <i>48th International Colloquium on Automata, Languages, and Programming</i>, vol. 198, 124, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2021.124\">10.4230/LIPIcs.ICALP.2021.124</a>.","short":"K. Chatterjee, M.H. Henzinger, S.S. Kale, A. Svozil, in:, 48th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021.","ama":"Chatterjee K, Henzinger MH, Kale SS, Svozil A. Faster algorithms for bounded liveness in graphs and game graphs. In: <i>48th International Colloquium on Automata, Languages, and Programming</i>. Vol 198. Schloss Dagstuhl - Leibniz Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2021.124\">10.4230/LIPIcs.ICALP.2021.124</a>","chicago":"Chatterjee, Krishnendu, Monika H Henzinger, Sagar Sudhir Kale, and Alexander Svozil. “Faster Algorithms for Bounded Liveness in Graphs and Game Graphs.” In <i>48th International Colloquium on Automata, Languages, and Programming</i>, Vol. 198. Schloss Dagstuhl - Leibniz Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2021.124\">https://doi.org/10.4230/LIPIcs.ICALP.2021.124</a>.","ista":"Chatterjee K, Henzinger MH, Kale SS, Svozil A. 2021. Faster algorithms for bounded liveness in graphs and game graphs. 48th International Colloquium on Automata, Languages, and Programming. ICALP: International Colloquium on Automata, Languages, and Programming, LIPIcs, vol. 198, 124.","apa":"Chatterjee, K., Henzinger, M. H., Kale, S. S., &#38; Svozil, A. (2021). Faster algorithms for bounded liveness in graphs and game graphs. In <i>48th International Colloquium on Automata, Languages, and Programming</i> (Vol. 198). Glasgow, Scotland: Schloss Dagstuhl - Leibniz Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.ICALP.2021.124\">https://doi.org/10.4230/LIPIcs.ICALP.2021.124</a>"},"publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-195-5"]},"doi":"10.4230/LIPIcs.ICALP.2021.124","author":[{"orcid":"0000-0002-4561-241X","first_name":"Krishnendu","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H","first_name":"Monika H","last_name":"Henzinger"},{"last_name":"Kale","first_name":"Sagar Sudhir","full_name":"Kale, Sagar Sudhir"},{"first_name":"Alexander","last_name":"Svozil","full_name":"Svozil, Alexander"}],"publication":"48th International Colloquium on Automata, Languages, and Programming","has_accepted_license":"1","ddc":["000"],"project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818"}],"file_date_updated":"2021-10-01T08:49:26Z","acknowledgement":"Krishnendu Chatterjee: Supported by the ERC CoG 863818 (ForM-SMArt). Monika Henzinger: Supported by the Austrian Science Fund (FWF) and netIDEE SCIENCE project P 33775-N. Sagar Sudhir Kale: Partially supported by the Vienna Science and Technology Fund (WWTF) through project ICT15-003. Alexander Svozil: Fully supported by the Vienna Science and Technology Fund (WWTF) through project ICT15-003.","year":"2021","volume":198,"intvolume":"       198"}