{"year":"2025","license":"https://creativecommons.org/licenses/by/4.0/","OA_place":"publisher","article_processing_charge":"Yes","month":"04","acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093 and the Israel Science Foundation grant 2410/22. N. Mazzocchi was affiliated with ISTA when this work was submitted for publication.","scopus_import":"1","oa":1,"_id":"20342","file_date_updated":"2025-09-11T12:17:12Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"mla":"Boker, Udi, et al. “ Safety and Liveness of Quantitative Properties and Automata.” <i>Logical Methods in Computer Science</i>, vol. 21, no. 2, 13149, EPI Sciences, 2025, doi:<a href=\"https://doi.org/10.46298/lmcs-21(2:2)2025\">10.46298/lmcs-21(2:2)2025</a>.","chicago":"Boker, Udi, Thomas A Henzinger, Nicolas Adrien Mazzocchi, and Naci E Sarac. “ Safety and Liveness of Quantitative Properties and Automata.” <i>Logical Methods in Computer Science</i>. EPI Sciences, 2025. <a href=\"https://doi.org/10.46298/lmcs-21(2:2)2025\">https://doi.org/10.46298/lmcs-21(2:2)2025</a>.","apa":"Boker, U., Henzinger, T. A., Mazzocchi, N. A., &#38; Sarac, N. E. (2025).  Safety and liveness of quantitative properties and automata. <i>Logical Methods in Computer Science</i>. EPI Sciences. <a href=\"https://doi.org/10.46298/lmcs-21(2:2)2025\">https://doi.org/10.46298/lmcs-21(2:2)2025</a>","ista":"Boker U, Henzinger TA, Mazzocchi NA, Sarac NE. 2025.  Safety and liveness of quantitative properties and automata. Logical Methods in Computer Science. 21(2), 13149.","ieee":"U. Boker, T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “ Safety and liveness of quantitative properties and automata,” <i>Logical Methods in Computer Science</i>, vol. 21, no. 2. EPI Sciences, 2025.","ama":"Boker U, Henzinger TA, Mazzocchi NA, Sarac NE.  Safety and liveness of quantitative properties and automata. <i>Logical Methods in Computer Science</i>. 2025;21(2). doi:<a href=\"https://doi.org/10.46298/lmcs-21(2:2)2025\">10.46298/lmcs-21(2:2)2025</a>","short":"U. Boker, T.A. Henzinger, N.A. Mazzocchi, N.E. Sarac, Logical Methods in Computer Science 21 (2025)."},"DOAJ_listed":"1","language":[{"iso":"eng"}],"title":" Safety and liveness of quantitative properties and automata","isi":1,"project":[{"grant_number":"101020093","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","call_identifier":"H2020","name":"Vigilant Algorithmic Monitoring of Software"}],"author":[{"id":"31E297B6-F248-11E8-B48F-1D18A9856A87","last_name":"Boker","first_name":"Udi","full_name":"Boker, Udi"},{"first_name":"Thomas A","full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","orcid":"0000-0002-2985-7724"},{"id":"b26baa86-3308-11ec-87b0-8990f34baa85","last_name":"Mazzocchi","first_name":"Nicolas Adrien","full_name":"Mazzocchi, Nicolas Adrien"},{"first_name":"Naci E","full_name":"Sarac, Naci E","id":"8C6B42F8-C8E6-11E9-A03A-F2DCE5697425","last_name":"Sarac"}],"publication_identifier":{"eissn":["1860-5974"]},"date_updated":"2025-12-02T14:09:38Z","corr_author":"1","file":[{"relation":"main_file","content_type":"application/pdf","file_id":"20343","date_created":"2025-09-11T12:17:12Z","checksum":"0b4d477bd981379724c35a4de2c176e5","access_level":"open_access","creator":"esarac","file_name":"2307.06016.pdf","file_size":709584,"date_updated":"2025-09-11T12:17:12Z","success":1}],"ddc":["000"],"date_created":"2025-09-11T12:17:52Z","ec_funded":1,"arxiv":1,"publication":"Logical Methods in Computer Science","article_type":"original","quality_controlled":"1","article_number":"13149","status":"public","abstract":[{"lang":"eng","text":"Safety and liveness stand as fundamental concepts in formal languages, playing a key role in verification. The safety-liveness classification of boolean properties characterizes whether a given property can be falsified by observing a finite prefix of an infinite computation trace (always for safety, never for liveness). In the quantitative setting, properties are arbitrary functions from infinite words to partially-ordered domains. Extending this paradigm to the quantitative domain, where properties are arbitrary functions mapping infinite words to partially-ordered domains, we introduce and study the notions of quantitative safety and liveness. First, we formally define quantitative safety and liveness, and prove that our definitions induce conservative quantitative generalizations of both the safety-progress hierarchy and the safety-liveness decomposition of boolean properties. Consequently, like their boolean counterparts, quantitative properties can be min-decomposed into safety and liveness parts, or alternatively, max-decomposed into co-safety and co-liveness parts. We further establish a connection between quantitative safety and topological continuity and provide alternative characterizations of quantitative safety and liveness in terms of their boolean analogs. Second, we instantiate our framework with the specific classes of quantitative properties expressed by automata. These quantitative automata contain finitely many states and rational-valued transition weights, and their common value functions Inf, Sup, LimInf, LimSup, LimInfAvg, LimSupAvg, and DSum map infinite words into the totally-ordered domain of real numbers. For all common value functions, we provide a procedure for deciding whether a given automaton is safe or live, we show how to construct its safety closure, and we present a min-decomposition into safe and live automata."}],"intvolume":"        21","has_accepted_license":"1","related_material":{"record":[{"relation":"dissertation_contains","id":"20147","status":"public"},{"relation":"earlier_version","id":"13221","status":"public"}]},"type":"journal_article","external_id":{"isi":["001468887900001"],"arxiv":["2307.06016"]},"oa_version":"Published Version","doi":"10.46298/lmcs-21(2:2)2025","tmp":{"short":"CC BY (4.0)","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"},"PlanS_conform":"1","issue":"2","volume":21,"OA_type":"gold","date_published":"2025-04-08T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"ToHe"}],"publisher":"EPI Sciences","publication_status":"published","day":"08"}