{"year":"2026","ec_funded":1,"intvolume":"       391","keyword":["Runtime Verification","Probabilistic Systems","Quantitative Verification","Approximate Monitoring"],"month":"08","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Cano Cordoba, Filip","id":"708cad98-e86a-11ef-8098-bdae2d7c6af1","last_name":"Cano Cordoba","first_name":"Filip","orcid":"0000-0002-0783-904X"},{"orcid":"0000-0002-2985-7724","first_name":"Thomas A","full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","last_name":"Henzinger"},{"id":"8121a2d0-dc85-11ea-9058-af578f3b4515","last_name":"Kueffner","full_name":"Kueffner, Konstantin","first_name":"Konstantin","orcid":"0000-0001-8974-2542"},{"full_name":"Sarac, Naci E","id":"8C6B42F8-C8E6-11E9-A03A-F2DCE5697425","last_name":"Sarac","first_name":"Naci E"}],"day":"24","fulldoi":"https://doi.org/10.4230/LIPIcs.CONCUR.2026.22","OA_place":"publisher","file_date_updated":"2026-09-22T05:59:03Z","supplementarymaterial":"no","article_processing_charge":"Yes","conference":{"end_date":"2026-09-04","name":"CONCUR: Conference on Concurrency Theory","start_date":"2026-09-01","location":"Liverpool, United Kingdom"},"scopus_import":"1","abstract":[{"text":"Runtime monitoring of quantitative signals faces a fundamental trade-off between volatility and over-aggregation: instantaneous observations are noisy, while long-run averages obscure local structure. Localisation measures such as discounted averages offer a principled middle ground, yet remain poorly understood in runtime verification. This paper studies discounted sums from a monitoring perspective, in both deterministic and stochastic settings. We formalize the discounted monitoring problem and show that exact, sound monitoring of discounted sums cannot be achieved with finite memory. To overcome this impossibility, we introduce ε-approximately sound monitoring, deriving explicit bounds on memory and observation requirements. We then extend the framework to stochastic processes via expected discounted sums, defining pointwise and uniform (ε,δ)-soundness notions, establishing statistical optimality, and proving impossibility beyond a precision threshold. We also formalize the resource complexity of deterministic discounted monitoring via affine register machines and prove a tight worst-case lower bound. Finally, we present a specification language for arithmetic expressions over multiple discounted sums with synchronous and asynchronous semantics, and evaluate our approach on practical scenarios including algorithmic fairness.","lang":"eng"}],"_id":"22921","status":"public","dataavailabilitystatement":"Software (Source Code): https://github.com/filipcano/monitoringdiscounted-sum-properties [10]\r\narchived at swh:1:dir:cb99396415f279c985cd05206b44320227f64245\r\n","title":"Monitoring discounted sum properties","doi":"10.4230/LIPIcs.CONCUR.2026.22","project":[{"call_identifier":"H2020","grant_number":"101020093","_id":"62781420-2b32-11ec-9570-8d9b63373d4d","name":"Vigilant Algorithmic Monitoring of Software"}],"corr_author":"1","department":[{"_id":"ToHe"},{"_id":"GradSch"}],"file":[{"checksum":"f7b2e22428344fd7972c54f099df6aba","file_size":997156,"access_level":"open_access","date_updated":"2026-09-22T05:59:03Z","content_type":"application/pdf","creator":"dernst","file_id":"22978","relation":"main_file","date_created":"2026-09-22T05:59:03Z","success":1,"file_name":"2026_LIPIcsCONCUR_Cano.pdf"}],"quality_controlled":"1","date_published":"2026-08-24T00:00:00Z","oa":1,"has_accepted_license":"1","type":"conference","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"arxiv":1,"publication_status":"published","external_id":{"arxiv":["2606.25979"]},"publication":"37th International Conference on Concurrency Theory","OA_type":"gold","researchdata_availability":"no","oa_version":"Published Version","date_created":"2026-09-13T22:01:54Z","citation":{"chicago":"Cano Cordoba, Filip, Thomas A Henzinger, Konstantin Kueffner, and Naci E Sarac. “Monitoring Discounted Sum Properties.” In <i>37th International Conference on Concurrency Theory</i>, Vol. 391. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2026.22\">https://doi.org/10.4230/LIPIcs.CONCUR.2026.22</a>.","ama":"Cano Cordoba F, Henzinger TA, Kueffner K, Sarac NE. Monitoring discounted sum properties. In: <i>37th International Conference on Concurrency Theory</i>. Vol 391. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2026.22\">10.4230/LIPIcs.CONCUR.2026.22</a>","ieee":"F. Cano Cordoba, T. A. Henzinger, K. Kueffner, and N. E. Sarac, “Monitoring discounted sum properties,” in <i>37th International Conference on Concurrency Theory</i>, Liverpool, United Kingdom, 2026, vol. 391.","apa":"Cano Cordoba, F., Henzinger, T. A., Kueffner, K., &#38; Sarac, N. E. (2026). Monitoring discounted sum properties. In <i>37th International Conference on Concurrency Theory</i> (Vol. 391). Liverpool, United Kingdom: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2026.22\">https://doi.org/10.4230/LIPIcs.CONCUR.2026.22</a>","mla":"Cano Cordoba, Filip, et al. “Monitoring Discounted Sum Properties.” <i>37th International Conference on Concurrency Theory</i>, vol. 391, 22:1-22:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPIcs.CONCUR.2026.22\">10.4230/LIPIcs.CONCUR.2026.22</a>.","ista":"Cano Cordoba F, Henzinger TA, Kueffner K, Sarac NE. 2026. Monitoring discounted sum properties. 37th International Conference on Concurrency Theory. CONCUR: Conference on Concurrency Theory, LIPIcs, vol. 391, 22:1-22:19.","short":"F. Cano Cordoba, T.A. Henzinger, K. Kueffner, N.E. Sarac, in:, 37th International Conference on Concurrency Theory, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026."},"article_number":"22:1-22:19","language":[{"iso":"eng"}],"date_updated":"2026-09-22T06:02:06Z","das_tickbox":"1","acknowledgement":"This work has been supported by the European Research Council under Grant No.: ERC2020-AdG 101020093 and ERC-2021-AdG 101055412.\r\nFilip Cano: ERC-2020-AdG 101020093\r\nThomas A. Henzinger: ERC-2020-AdG 101020093\r\nKonstantin Kueffner: ERC-2020-AdG 101020093\r\nN. Ege Saraç: ERC-2021-AdG 101055412","volume":391,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"publication_identifier":{"isbn":["9783959774475"],"issn":["1868-8969"]},"ddc":["000"]}