{"license":"https://creativecommons.org/licenses/by/4.0/","oa_version":"Published Version","keyword":["Theoretical Computer Science","Software"],"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"external_id":{"arxiv":["2108.02188"]},"oa":1,"has_accepted_license":"1","publisher":"Association for Computing Machinery","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"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","publication_identifier":{"issn":["0934-5043"],"eissn":["1433-299X"]},"intvolume":"        35","year":"2023","language":[{"iso":"eng"}],"date_updated":"2024-01-17T08:19:41Z","day":"23","publication":"Formal Aspects of Computing","ec_funded":1,"doi":"10.1145/3585391","file_date_updated":"2024-01-16T08:11:24Z","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.","date_created":"2024-01-10T09:27:43Z","date_published":"2023-06-23T00:00:00Z","title":"On lexicographic proof rules for probabilistic termination","project":[{"_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","call_identifier":"H2020","grant_number":"863818"},{"call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"citation":{"short":"K. Chatterjee, E. Kafshdar Goharshady, P. Novotný, J. Zárevúcky, D. Zikelic, Formal Aspects of Computing 35 (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>.","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>","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.","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>","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>."},"month":"06","author":[{"full_name":"Chatterjee, Krishnendu","last_name":"Chatterjee","first_name":"Krishnendu","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4561-241X"},{"full_name":"Kafshdar Goharshady, Ehsan","first_name":"Ehsan","last_name":"Kafshdar Goharshady"},{"id":"3CC3B868-F248-11E8-B48F-1D18A9856A87","first_name":"Petr","last_name":"Novotný","full_name":"Novotný, Petr"},{"first_name":"Jiří","last_name":"Zárevúcky","full_name":"Zárevúcky, Jiří"},{"orcid":"0000-0002-4681-1699","id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","first_name":"Dorde","last_name":"Zikelic","full_name":"Zikelic, Dorde"}],"related_material":{"record":[{"relation":"earlier_version","id":"10414","status":"public"}]},"article_number":"11","quality_controlled":"1","publication_status":"published","volume":35,"_id":"14778","file":[{"file_name":"2023_FormalAspectsComputing_Chatterjee.pdf","access_level":"open_access","checksum":"3bb133eeb27ec01649a9a36445d952d9","content_type":"application/pdf","success":1,"creator":"dernst","date_updated":"2024-01-16T08:11:24Z","file_size":502522,"relation":"main_file","date_created":"2024-01-16T08:11:24Z","file_id":"14804"}],"status":"public","article_processing_charge":"Yes (via OA deal)","ddc":["000"],"type":"journal_article","issue":"2","department":[{"_id":"KrCh"}]}