{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T13:39:56Z","timestamp":1774964396969,"version":"3.50.1"},"reference-count":33,"publisher":"Association for Computing Machinery (ACM)","issue":"5s","funder":[{"name":"Hong Kong RGC GRF","award":["14201924"],"award-info":[{"award-number":["14201924"]}]},{"DOI":"10.13039\/100000001","name":"U.S. National Science Foundation","doi-asserted-by":"crossref","award":["CCF-1954837 and CNS-2153056"],"award-info":[{"award-number":["CCF-1954837 and CNS-2153056"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100000183","name":"U.S. Army Research Office","doi-asserted-by":"crossref","award":["W911NF2410082"],"award-info":[{"award-number":["W911NF2410082"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001821","name":"Vienna Science and Technology Fund","doi-asserted-by":"crossref","award":["10.47379\/ICT22-023] (TAIGER)"],"award-info":[{"award-number":["10.47379\/ICT22-023] (TAIGER)"]}],"id":[{"id":"10.13039\/501100001821","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Embed. Comput. Syst."],"published-print":{"date-parts":[[2025,9,30]]},"abstract":"<jats:p>\n            Signal Temporal Logic (STL) is a widely adopted specification language for Cyber-Physical Systems that can be used to express critical temporal requirements, such as system safety and response time. STL\u2019s expressivity, however, is not sufficient to capture the cumulative duration during which a property holds within an interval of time. To overcome this limitation, we introduce\n            <jats:italic toggle=\"yes\">Cumulative-Time Signal Temporal Logic<\/jats:italic>\n            (CT-STL) which operates over discrete-time signals and extends STL with a new\n            <jats:italic toggle=\"yes\">cumulative-time<\/jats:italic>\n            operator. This operator compares the sum of all timesteps for which its nested formula is true with a threshold. We present both a qualitative and a quantitative (robustness) semantics for CT-STL and prove the soundness and completeness of the robustness semantics. We also provide an efficient online monitoring algorithm for both semantics. We demonstrate the utility of CT-STL via two case studies: specifying and monitoring cumulative temporal requirements for a microgrid and an artificial pancreas.\n          <\/jats:p>","DOI":"10.1145\/3763237","type":"journal-article","created":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T11:25:51Z","timestamp":1756121151000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Cumulative-Time Signal Temporal Logic"],"prefix":"10.1145","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7206-6584","authenticated-orcid":false,"given":"Hongkai","family":"Chen","sequence":"first","affiliation":[{"name":"Information Engineering, The Chinese University of Hong Kong","place":["Hong Kong, Hong Kong"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6744-901X","authenticated-orcid":false,"given":"Zeyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering, Stony Brook University","place":["Stony Brook, United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4953-1571","authenticated-orcid":false,"given":"Shouvik","family":"Roy","sequence":"additional","affiliation":[{"name":"Illinois Institute of Technology","place":["Chicago, United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8004-6601","authenticated-orcid":false,"given":"Ezio","family":"Bartocci","sequence":"additional","affiliation":[{"name":"TU Wien","place":["Vienna, Austria"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7348-630X","authenticated-orcid":false,"given":"Scott A.","family":"Smolka","sequence":"additional","affiliation":[{"name":"Computer Science, Stony Brook University","place":["Stony Brook, United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8824-6835","authenticated-orcid":false,"given":"Scott","family":"Stoller","sequence":"additional","affiliation":[{"name":"Computer Science, Stony Brook University","place":["Stony Brook, United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6362-2972","authenticated-orcid":false,"given":"Shan","family":"Lin","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering, Stony Brook University","place":["Stony Brook, United States"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2025,9,26]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-21668-3_21"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/227595.227602"},{"key":"e_1_3_3_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-75632-5_5"},{"key":"e_1_3_3_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/3178126.3178131"},{"key":"e_1_3_3_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/S10009-020-00599-4"},{"key":"e_1_3_3_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICST57152.2023.00029"},{"key":"e_1_3_3_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(73)80033-9"},{"key":"e_1_3_3_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-15839-1_7"},{"key":"e_1_3_3_10_2","doi-asserted-by":"publisher","DOI":"10.1145\/3575870.3587119"},{"key":"e_1_3_3_11_2","doi-asserted-by":"publisher","DOI":"10.2337\/dc24-S006"},{"key":"e_1_3_3_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10703-017-0286-7"},{"key":"e_1_3_3_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39799-8_19"},{"key":"e_1_3_3_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15297-9_9"},{"key":"e_1_3_3_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-32079-9_3"},{"key":"e_1_3_3_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/J.TCS.2009.06.021"},{"key":"e_1_3_3_17_2","doi-asserted-by":"publisher","DOI":"10.1109\/CDC40024.2019.9029429"},{"key":"e_1_3_3_18_2","volume-title":"IEEE Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces","year":"2018","unstructured":"IEEE 1547-2018. 2018. 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