[{"oa_version":"Preprint","year":"2021","external_id":{"isi":["000758218600033"],"arxiv":["2108.02188"]},"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2025-07-14T09:10:11Z","publication_identifier":{"eisbn":["978-3-030-90870-6"],"isbn":["9-783-0309-0869-0"],"issn":["0302-9743"],"eissn":["1611-3349"]},"arxiv":1,"article_processing_charge":"No","_id":"10414","date_published":"2021-11-10T00:00:00Z","abstract":[{"lang":"eng","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 LexRSM not existing even for simple terminating programs. Our contributions are twofold: First, we introduce a generalization of LexRSMs which 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."}],"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2108.02188"}],"oa":1,"volume":13047,"citation":{"ama":"Chatterjee K, Goharshady EK, Novotný P, Zárevúcky J, Zikelic D. On lexicographic proof rules for probabilistic termination. In: <i>24th International Symposium on Formal Methods</i>. Vol 13047. Springer Nature; 2021:619-639. doi:<a href=\"https://doi.org/10.1007/978-3-030-90870-6_33\">10.1007/978-3-030-90870-6_33</a>","apa":"Chatterjee, K., Goharshady, E. K., Novotný, P., Zárevúcky, J., &#38; Zikelic, D. (2021). On lexicographic proof rules for probabilistic termination. In <i>24th International Symposium on Formal Methods</i> (Vol. 13047, pp. 619–639). Virtual: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-90870-6_33\">https://doi.org/10.1007/978-3-030-90870-6_33</a>","short":"K. Chatterjee, E.K. Goharshady, P. Novotný, J. Zárevúcky, D. Zikelic, in:, 24th International Symposium on Formal Methods, Springer Nature, 2021, pp. 619–639.","mla":"Chatterjee, Krishnendu, et al. “On Lexicographic Proof Rules for Probabilistic Termination.” <i>24th International Symposium on Formal Methods</i>, vol. 13047, Springer Nature, 2021, pp. 619–39, doi:<a href=\"https://doi.org/10.1007/978-3-030-90870-6_33\">10.1007/978-3-030-90870-6_33</a>.","chicago":"Chatterjee, Krishnendu, Ehsan Kafshdar Goharshady, Petr Novotný, Jiří Zárevúcky, and Dorde Zikelic. “On Lexicographic Proof Rules for Probabilistic Termination.” In <i>24th International Symposium on Formal Methods</i>, 13047:619–39. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/978-3-030-90870-6_33\">https://doi.org/10.1007/978-3-030-90870-6_33</a>.","ieee":"K. Chatterjee, E. K. Goharshady, P. Novotný, J. Zárevúcky, and D. Zikelic, “On lexicographic proof rules for probabilistic termination,” in <i>24th International Symposium on Formal Methods</i>, Virtual, 2021, vol. 13047, pp. 619–639.","ista":"Chatterjee K, Goharshady EK, Novotný P, Zárevúcky J, Zikelic D. 2021. On lexicographic proof rules for probabilistic termination. 24th International Symposium on Formal Methods. FM: Formal Methods, LNCS, vol. 13047, 619–639."},"ec_funded":1,"title":"On lexicographic proof rules for probabilistic termination","conference":{"location":"Virtual","name":"FM: Formal Methods","start_date":"2021-11-20","end_date":"2021-11-26"},"day":"10","author":[{"orcid":"0000-0002-4561-241X","id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","first_name":"Krishnendu"},{"last_name":"Goharshady","full_name":"Goharshady, Ehsan Kafshdar","first_name":"Ehsan Kafshdar"},{"id":"3CC3B868-F248-11E8-B48F-1D18A9856A87","full_name":"Novotný, Petr","first_name":"Petr","last_name":"Novotný"},{"full_name":"Zárevúcky, Jiří","first_name":"Jiří","last_name":"Zárevúcky"},{"id":"294AA7A6-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4681-1699","last_name":"Zikelic","full_name":"Zikelic, Dorde","first_name":"Dorde"}],"type":"conference","alternative_title":["LNCS"],"project":[{"call_identifier":"H2020","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","name":"Formal Methods for Stochastic Models: Algorithms and Applications","grant_number":"863818"},{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"14539","status":"public"},{"relation":"later_version","id":"14778","status":"public"}]},"acknowledgement":"This research was partially supported by the ERC CoG 863818 (ForM-SMArt), the Czech Science Foundation grant No. GJ19-15134Y, and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385.","language":[{"iso":"eng"}],"doi":"10.1007/978-3-030-90870-6_33","page":"619-639","month":"11","date_created":"2021-12-05T23:01:45Z","publisher":"Springer Nature","isi":1,"publication":"24th International Symposium on Formal Methods","quality_controlled":"1","department":[{"_id":"KrCh"}],"status":"public","intvolume":"     13047"}]