[{"oa_version":"Published Version","year":"2023","has_accepted_license":"1","article_type":"original","publication_identifier":{"issn":["0934-5043"],"eissn":["1433-299X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-07-14T09:10:10Z","external_id":{"arxiv":["2108.02188"]},"date_published":"2023-06-23T00:00:00Z","_id":"14778","abstract":[{"text":"We consider the almost-sure (a.s.) termination problem for probabilistic programs, which are a stochastic extension of classical imperative programs. Lexicographic ranking functions provide a sound and practical approach for termination of non-probabilistic programs, and their extension to probabilistic programs is achieved via lexicographic ranking supermartingales (LexRSMs). However, LexRSMs introduced in the previous work have a limitation that impedes their automation: all of their components have to be non-negative in all reachable states. This might result in a LexRSM not existing even for simple terminating programs. Our contributions are twofold. First, we introduce a generalization of LexRSMs that allows for some components to be negative. This standard feature of non-probabilistic termination proofs was hitherto not known to be sound in the probabilistic setting, as the soundness proof requires a careful analysis of the underlying stochastic process. Second, we present polynomial-time algorithms using our generalized LexRSMs for proving a.s. termination in broad classes of linear-arithmetic programs.","lang":"eng"}],"file":[{"access_level":"open_access","date_updated":"2024-01-16T08:11:24Z","checksum":"3bb133eeb27ec01649a9a36445d952d9","creator":"dernst","file_size":502522,"file_name":"2023_FormalAspectsComputing_Chatterjee.pdf","success":1,"date_created":"2024-01-16T08:11:24Z","relation":"main_file","file_id":"14804","content_type":"application/pdf"}],"article_number":"11","issue":"2","article_processing_charge":"Yes (via OA deal)","arxiv":1,"volume":35,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"file_date_updated":"2024-01-16T08:11:24Z","oa":1,"publication_status":"published","author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X","last_name":"Chatterjee","first_name":"Krishnendu","full_name":"Chatterjee, Krishnendu"},{"last_name":"Kafshdar Goharshady","first_name":"Ehsan","full_name":"Kafshdar Goharshady, Ehsan"},{"first_name":"Petr","full_name":"Novotný, Petr","last_name":"Novotný","id":"3CC3B868-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Zárevúcky","first_name":"Jiří","full_name":"Zárevúcky, Jiří"},{"first_name":"Dorde","full_name":"Zikelic, Dorde","last_name":"Zikelic","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699"}],"type":"journal_article","day":"23","title":"On lexicographic proof rules for probabilistic termination","ec_funded":1,"citation":{"mla":"Chatterjee, Krishnendu, et al. “On Lexicographic Proof Rules for Probabilistic Termination.” <i>Formal Aspects of Computing</i>, vol. 35, no. 2, 11, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3585391\">10.1145/3585391</a>.","ista":"Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. 2023. On lexicographic proof rules for probabilistic termination. Formal Aspects of Computing. 35(2), 11.","ieee":"K. Chatterjee, E. Kafshdar Goharshady, P. Novotný, J. Zárevúcky, and D. Zikelic, “On lexicographic proof rules for probabilistic termination,” <i>Formal Aspects of Computing</i>, vol. 35, no. 2. Association for Computing Machinery, 2023.","chicago":"Chatterjee, Krishnendu, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, and Dorde Zikelic. “On Lexicographic Proof Rules for Probabilistic Termination.” <i>Formal Aspects of Computing</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3585391\">https://doi.org/10.1145/3585391</a>.","apa":"Chatterjee, K., Kafshdar Goharshady, E., Novotný, P., Zárevúcky, J., &#38; Zikelic, D. (2023). On lexicographic proof rules for probabilistic termination. <i>Formal Aspects of Computing</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3585391\">https://doi.org/10.1145/3585391</a>","ama":"Chatterjee K, Kafshdar Goharshady E, Novotný P, Zárevúcky J, Zikelic D. On lexicographic proof rules for probabilistic termination. <i>Formal Aspects of Computing</i>. 2023;35(2). doi:<a href=\"https://doi.org/10.1145/3585391\">10.1145/3585391</a>","short":"K. Chatterjee, E. Kafshdar Goharshady, P. Novotný, J. Zárevúcky, D. Zikelic, Formal Aspects of Computing 35 (2023)."},"ddc":["000"],"doi":"10.1145/3585391","language":[{"iso":"eng"}],"keyword":["Theoretical Computer Science","Software"],"acknowledgement":"This research was partially supported by the ERC CoG (grant no. 863818; ForM-SMArt), the Czech Science Foundation (grant no. GA21-24711S), and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 665385.","project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","name":"Formal Methods for Stochastic Models: Algorithms and Applications"},{"grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10414"}]},"date_created":"2024-01-10T09:27:43Z","month":"06","status":"public","intvolume":"        35","department":[{"_id":"KrCh"}],"quality_controlled":"1","publication":"Formal Aspects of Computing","publisher":"Association for Computing Machinery"}]