{"author":[{"full_name":"Henzinger, Thomas A","orcid":"0000-0002-2985-7724","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger","first_name":"Thomas A"},{"full_name":"Mazzocchi, Nicolas Adrien","id":"b26baa86-3308-11ec-87b0-8990f34baa85","first_name":"Nicolas Adrien","last_name":"Mazzocchi"},{"last_name":"Sarac","first_name":"Naci E","id":"8C6B42F8-C8E6-11E9-A03A-F2DCE5697425","full_name":"Sarac, Naci E"}],"page":"349-370","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"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"}],"year":"2023","acknowledgement":"We thank the anonymous reviewers for their helpful comments. This work was supported in part by the ERC-2020-AdG 101020093.","oa":1,"publication_identifier":{"eissn":["1611-3349"],"isbn":["9783031308284"],"issn":["0302-9743"]},"isi":1,"article_processing_charge":"No","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2023-04-21T00:00:00Z","has_accepted_license":"1","_id":"12467","type":"conference","quality_controlled":"1","publication_status":"published","month":"04","oa_version":"Published Version","date_updated":"2025-09-09T12:21:08Z","title":"Quantitative safety and liveness","doi":"10.1007/978-3-031-30829-1_17","external_id":{"isi":["001288609300017"],"arxiv":["2301.11175"]},"intvolume":"     13992","publication":"26th International Conference Foundations of Software Science and Computation Structures","alternative_title":["LNCS"],"file_date_updated":"2023-06-19T10:28:09Z","department":[{"_id":"GradSch"},{"_id":"ToHe"}],"project":[{"_id":"62781420-2b32-11ec-9570-8d9b63373d4d","name":"Vigilant Algorithmic Monitoring of Software","call_identifier":"H2020","grant_number":"101020093"}],"ec_funded":1,"citation":{"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.","chicago":"Henzinger, Thomas A, Nicolas Adrien Mazzocchi, and Naci E Sarac. “Quantitative Safety and Liveness.” In <i>26th International Conference Foundations of Software Science and Computation Structures</i>, 13992:349–70. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/978-3-031-30829-1_17\">https://doi.org/10.1007/978-3-031-30829-1_17</a>.","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.","ieee":"T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “Quantitative safety and liveness,” in <i>26th International Conference Foundations of Software Science and Computation Structures</i>, Paris, France, 2023, vol. 13992, pp. 349–370.","apa":"Henzinger, T. A., Mazzocchi, N. A., &#38; Sarac, N. E. (2023). Quantitative safety and liveness. In <i>26th International Conference Foundations of Software Science and Computation Structures</i> (Vol. 13992, pp. 349–370). Paris, France: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-30829-1_17\">https://doi.org/10.1007/978-3-031-30829-1_17</a>","ama":"Henzinger TA, Mazzocchi NA, Sarac NE. Quantitative safety and liveness. In: <i>26th International Conference Foundations of Software Science and Computation Structures</i>. Vol 13992. Springer Nature; 2023:349-370. doi:<a href=\"https://doi.org/10.1007/978-3-031-30829-1_17\">10.1007/978-3-031-30829-1_17</a>","mla":"Henzinger, Thomas A., et al. “Quantitative Safety and Liveness.” <i>26th International Conference Foundations of Software Science and Computation Structures</i>, vol. 13992, Springer Nature, 2023, pp. 349–70, doi:<a href=\"https://doi.org/10.1007/978-3-031-30829-1_17\">10.1007/978-3-031-30829-1_17</a>."},"corr_author":"1","file":[{"date_created":"2023-01-31T07:22:21Z","relation":"main_file","checksum":"981025aed580b6b27c426cb8856cf63e","file_name":"qsl.pdf","file_size":449027,"file_id":"12468","content_type":"application/pdf","creator":"esarac","access_level":"open_access","success":1,"date_updated":"2023-01-31T07:22:21Z"},{"checksum":"f16e2af1e0eb243158ab0f0fe74e7d5a","relation":"main_file","date_created":"2023-06-19T10:28:09Z","file_size":1048171,"file_id":"13153","file_name":"2023_LNCS_HenzingerT.pdf","creator":"dernst","success":1,"access_level":"open_access","content_type":"application/pdf","date_updated":"2023-06-19T10:28:09Z"}],"scopus_import":"1","conference":{"name":"FOSSACS: Foundations of Software Science and Computation Structures","end_date":"2023-04-27","location":"Paris, France","start_date":"2023-04-22"},"ddc":["000"],"day":"21","language":[{"iso":"eng"}],"publisher":"Springer Nature","volume":13992,"status":"public","arxiv":1,"date_created":"2023-01-31T07:23:56Z"}