[{"page":"349-370","file":[{"content_type":"application/pdf","checksum":"981025aed580b6b27c426cb8856cf63e","file_size":449027,"date_created":"2023-01-31T07:22:21Z","creator":"esarac","relation":"main_file","file_id":"12468","success":1,"date_updated":"2023-01-31T07:22:21Z","file_name":"qsl.pdf","access_level":"open_access"},{"date_created":"2023-06-19T10:28:09Z","creator":"dernst","relation":"main_file","date_updated":"2023-06-19T10:28:09Z","access_level":"open_access","file_name":"2023_LNCS_HenzingerT.pdf","file_id":"13153","success":1,"content_type":"application/pdf","checksum":"f16e2af1e0eb243158ab0f0fe74e7d5a","file_size":1048171}],"citation":{"ieee":"T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “Quantitative safety and liveness,” in 26th International Conference Foundations of Software Science and Computation Structures, Paris, France, 2023, vol. 13992, pp. 349–370.","short":"T.A. Henzinger, N.A. Mazzocchi, N.E. Sarac, in:, 26th International Conference Foundations of Software Science and Computation Structures, Springer Nature, 2023, pp. 349–370.","mla":"Henzinger, Thomas A., et al. “Quantitative Safety and Liveness.” 26th International Conference Foundations of Software Science and Computation Structures, vol. 13992, Springer Nature, 2023, pp. 349–70, doi:10.1007/978-3-031-30829-1_17.","chicago":"Henzinger, Thomas A, Nicolas Adrien Mazzocchi, and Naci E Sarac. “Quantitative Safety and Liveness.” In 26th International Conference Foundations of Software Science and Computation Structures, 13992:349–70. Springer Nature, 2023. https://doi.org/10.1007/978-3-031-30829-1_17.","ista":"Henzinger TA, Mazzocchi NA, Sarac NE. 2023. Quantitative safety and liveness. 26th International Conference Foundations of Software Science and Computation Structures. FOSSACS: Foundations of Software Science and Computation Structures, LNCS, vol. 13992, 349–370.","ama":"Henzinger TA, Mazzocchi NA, Sarac NE. Quantitative safety and liveness. In: 26th International Conference Foundations of Software Science and Computation Structures. Vol 13992. Springer Nature; 2023:349-370. doi:10.1007/978-3-031-30829-1_17","apa":"Henzinger, T. A., Mazzocchi, N. A., & Sarac, N. E. (2023). Quantitative safety and liveness. In 26th International Conference Foundations of Software Science and Computation Structures (Vol. 13992, pp. 349–370). Paris, France: Springer Nature. https://doi.org/10.1007/978-3-031-30829-1_17"},"status":"public","title":"Quantitative safety and liveness","corr_author":"1","quality_controlled":"1","oa_version":"Published Version","day":"21","external_id":{"isi":["001288609300017"],"arxiv":["2301.11175"]},"oa":1,"isi":1,"publisher":"Springer Nature","publication":"26th International Conference Foundations of Software Science and Computation Structures","type":"conference","volume":13992,"arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2023-04-21T00:00:00Z","language":[{"iso":"eng"}],"date_updated":"2025-09-09T12:21:08Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2023","month":"04","project":[{"grant_number":"101020093","name":"Vigilant Algorithmic Monitoring of Software","call_identifier":"H2020","_id":"62781420-2b32-11ec-9570-8d9b63373d4d"}],"acknowledgement":"We thank the anonymous reviewers for their helpful comments. This work was supported in part by the ERC-2020-AdG 101020093.","intvolume":" 13992","author":[{"full_name":"Henzinger, Thomas A","last_name":"Henzinger","orcid":"0000-0002-2985-7724","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A"},{"full_name":"Mazzocchi, Nicolas Adrien","first_name":"Nicolas Adrien","last_name":"Mazzocchi","id":"b26baa86-3308-11ec-87b0-8990f34baa85"},{"id":"8C6B42F8-C8E6-11E9-A03A-F2DCE5697425","last_name":"Sarac","first_name":"Naci E","full_name":"Sarac, Naci E"}],"date_created":"2023-01-31T07:23:56Z","ddc":["000"],"has_accepted_license":"1","publication_status":"published","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["9783031308284"]},"alternative_title":["LNCS"],"_id":"12467","article_processing_charge":"No","file_date_updated":"2023-06-19T10:28:09Z","ec_funded":1,"abstract":[{"text":"Safety and liveness are elementary concepts of computation, and the foundation of many verification paradigms. 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 quantitative specification and verification, properties assign not truth values, but quantitative values to infinite traces (e.g., a cost, or the distance to a boolean property). We introduce quantitative safety and liveness, and we prove that our definitions induce conservative quantitative generalizations of both (1)~the safety-progress hierarchy of boolean properties and (2)~the safety-liveness decomposition of boolean properties. In particular, we show that every quantitative property can be written as the pointwise minimum of a quantitative safety property and a quantitative liveness property. Consequently, like boolean properties, also quantitative properties can be min-decomposed into safety and liveness parts, or alternatively, max-decomposed into co-safety and co-liveness parts. Moreover, quantitative properties can be approximated naturally. We prove that every quantitative property that has both safe and co-safe approximations can be monitored arbitrarily precisely by a monitor that uses only a finite number of states.","lang":"eng"}],"scopus_import":"1","conference":{"end_date":"2023-04-27","start_date":"2023-04-22","name":"FOSSACS: Foundations of Software Science and Computation Structures","location":"Paris, France"},"doi":"10.1007/978-3-031-30829-1_17","department":[{"_id":"GradSch"},{"_id":"ToHe"}]}]