{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:49:28Z","timestamp":1782348568373,"version":"3.54.5"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:00:00Z","timestamp":1782345600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:00:00Z","timestamp":1782345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100007082","name":"Universidade Federal De Santa Catarina","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007082","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Event Dyn Syst"],"published-print":{"date-parts":[[2026,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Cyber-physical systems (CPSs) are formed of physical and computational components that interact to operate a process safely and efficiently according to the desired behavior. To do so, the plant is continuously monitored, and the information obtained from its components is transmitted to computer-based devices. The connection between the plant and the monitoring and control device is carried out using communication networks, which may be susceptible to cyber-attacks. In this paper, we consider that the communication channel used to transmit data from the plant to the monitoring and control device is vulnerable to attacks, and that the attacker eavesdrops on the communication channel to gather sensitive information and discover if the system has reached a secret state. Since we assume that the information transmitted in the network is the status of system components, such as sensors, actuators, and memory variables of local controllers, the system can be modeled, from the attacker\u2019s perspective, as a finite state transducer, where each state of the model is associated with an output vector formed of the signals associated with the system components. Considering that the attacker has full knowledge of the system model and does not know the current state of the system when he\/she initiates to eavesdrop on the communication channel, the attacker tries to estimate the current state of the system by observing the state outputs transmitted in the network. Therefore, in this case, it is necessary to verify whether the attacker is never able to detect the secret states of the system. In the Discrete-Event System literature, the system property associated with the intruder\u2019s inability to discover the system secret based on the transmitted information is called opacity. Since, in this paper, the attacker observes state outputs of a finite state transducer instead of events, we introduce a new notion of opacity called Current-State Opacity based on State Outputs (CSO-SO). We also present a method for the verification of CSO-SO. In addition, a comparison between the definition of current-state opacity based on event observations and CSO-SO is provided. A practical system is used to illustrate the definition and verification of CSO-SO.<\/jats:p>","DOI":"10.1007\/s10626-026-00444-x","type":"journal-article","created":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:31:51Z","timestamp":1782347511000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Current-State opacity based on state outputs: definition and verification"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3100-0815","authenticated-orcid":false,"given":"Patr\u00edcia","family":"C. Mayer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1676-9805","authenticated-orcid":false,"given":"Felipe","family":"G. Cabral","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8168-2469","authenticated-orcid":false,"given":"Publio","family":"M. M. Lima","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5661-2637","authenticated-orcid":false,"given":"Marcos","family":"V. Moreira","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,25]]},"reference":[{"key":"444_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2021.109836","volume":"133","author":"RJ Barcelos","year":"2021","unstructured":"Barcelos RJ, Basilio JC (2021) Enforcing current-state opacity through shuffle and deletions of event observations. Automatica 133:109836","journal-title":"Automatica"},{"key":"444_CR2","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/j.automatica.2018.07.017","volume":"97","author":"LK Carvalho","year":"2018","unstructured":"Carvalho LK, Wu Y-C, Kwong R, Lafortune S (2018) Detection and mitigation of classes of attacks in supervisory control systems. Automatica 97:121\u2013133","journal-title":"Automatica"},{"key":"444_CR3","doi-asserted-by":"crossref","unstructured":"Cassandras CG, Lafortune S (2008) Introduction to discrete event system. Springer","DOI":"10.1007\/978-0-387-68612-7"},{"issue":"4","key":"444_CR4","doi-asserted-by":"publisher","first-page":"338","DOI":"10.7227\/IJEEE.42.4.5","volume":"42","author":"A Esmoris","year":"2005","unstructured":"Esmoris A, Ches\u00f1evar CI, Gonz\u00e1lez MP (2005) TAGS: a software tool for simulating transducer automata. Int J Electr Eng Educ 42(4):338\u2013349","journal-title":"Int J Electr Eng Educ"},{"key":"444_CR5","unstructured":"FESTO website. https:\/\/www.festo.com\/. Accessed: 25 Oct 2024"},{"issue":"7","key":"444_CR6","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/j.ifacol.2018.06.314","volume":"51","author":"R Fritz","year":"2018","unstructured":"Fritz R, Zhang P (2018) Modeling and detection of cyber attacks on discrete event systems. IFAC-PapersOnLine 51(7):285\u2013290","journal-title":"IFAC-PapersOnLine"},{"key":"444_CR7","doi-asserted-by":"crossref","unstructured":"Fritz R, Fauser M, Zhang P (2019) Controller encryption for discrete event systems. In: 2019 American control conference (ACC), Philadelphia, CA, USA, pp. 5633\u20135638","DOI":"10.23919\/ACC.2019.8814612"},{"key":"444_CR8","doi-asserted-by":"crossref","unstructured":"Gao C, Seatzu C, Li Z, Giua A (2019) Multiple attacks detection on discrete event systems. Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics 2019-October, 2352\u20132357","DOI":"10.1109\/SMC.2019.8914035"},{"key":"444_CR9","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.arcontrol.2016.04.015","volume":"41","author":"R Jacob","year":"2016","unstructured":"Jacob R, Lesage J-J, Faure J-M (2016) Overview of discrete event systems opacity: models, validation, and quantification. Annu Rev Control 41:135\u2013146","journal-title":"Annu Rev Control"},{"key":"444_CR10","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1016\/j.automatica.2018.03.041","volume":"93","author":"Y Ji","year":"2018","unstructured":"Ji Y, Wu Y-C, Lafortune S (2018) Enforcement of opacity by public and private insertion functions. Automatica 93:369\u2013378","journal-title":"Automatica"},{"key":"444_CR11","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/j.arcontrol.2018.04.002","volume":"45","author":"S Lafortune","year":"2018","unstructured":"Lafortune S, Lin F, Hadjicostis CN (2018) On the history of diagnosability and opacity in discrete event systems. Annu Rev Control 45:257\u2013266","journal-title":"Annu Rev Control"},{"issue":"10","key":"444_CR12","doi-asserted-by":"publisher","first-page":"5289","DOI":"10.1109\/TAC.2021.3121249","volume":"67","author":"X Li","year":"2022","unstructured":"Li X, Hadjicostis CN, Li Z (2022) Extended insertion functions for opacity enforcement in Discrete-Event Systems. IEEE Trans Autom Control 67(10):5289\u20135303","journal-title":"IEEE Trans Autom Control"},{"issue":"1","key":"444_CR13","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s40313-018-0420-9","volume":"30","author":"PM Lima","year":"2019","unstructured":"Lima PM, Alves MVS, Carvalho LK, Moreira MV (2019) Security against communication network attacks of cyber-physical systems. Journal of Control Automation and Electrical Systems 30(1):125\u2013135","journal-title":"Journal of Control Automation and Electrical Systems"},{"issue":"3","key":"444_CR14","doi-asserted-by":"publisher","first-page":"2030","DOI":"10.1109\/TASE.2021.3076697","volume":"19","author":"PM Lima","year":"2021","unstructured":"Lima PM, Alves MV, Carvalho LK, Moreira MV (2021) Security of cyber-physical systems: design of a security supervisor to thwart attacks. IEEE Trans Autom Sci Eng 19(3):2030\u20132041","journal-title":"IEEE Trans Autom Sci Eng"},{"issue":"28","key":"444_CR15","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.ifacol.2022.10.324","volume":"55","author":"PM Lima","year":"2022","unstructured":"Lima PM, da Silva CKP, de Farias CM, Carvalho LK, Moreira MV (2022) Event-based cryptography for automation networks of cyber-physical systems using the stream cipher ChaCha20. IFAC-PapersOnLine 55(28):58\u201365","journal-title":"IFAC-PapersOnLine"},{"key":"444_CR16","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.ins.2022.11.100","volume":"621","author":"PM Lima","year":"2023","unstructured":"Lima PM, Carvalho LK, Moreira MV (2023) Ensuring confidentiality of cyber-physical systems using event-based cryptography. Inf Sci 621:119\u2013135","journal-title":"Inf Sci"},{"issue":"3","key":"444_CR17","doi-asserted-by":"publisher","first-page":"496","DOI":"10.1016\/j.automatica.2011.01.002","volume":"47","author":"F Lin","year":"2011","unstructured":"Lin F (2011) Opacity of discrete event systems and its applications. Automatica 47(3):496\u2013503","journal-title":"Automatica"},{"key":"444_CR18","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.arcontrol.2022.03.004","volume":"53","author":"S Liu","year":"2022","unstructured":"Liu S, Trivedi A, Yin X, Zamani M (2022) Secure-by-construction synthesis of cyber-physical systems. Annu Rev Control 53:30\u201350","journal-title":"Annu Rev Control"},{"key":"444_CR19","doi-asserted-by":"crossref","unstructured":"Liu T, Seatzu C, Giua A (2023) Verification of current state opacity using switching output automata. In: 2023 9th International conference on control, decision and information technologies (CoDIT), pp 2665\u20132670","DOI":"10.1109\/CoDIT58514.2023.10284385"},{"key":"444_CR20","doi-asserted-by":"crossref","unstructured":"Machado THdM, Viana GS, Moreira MV (2023) Event-based automaton model for identification of discrete-event systems for fault detection. Control Eng Pract 134:105474","DOI":"10.1016\/j.conengprac.2023.105474"},{"key":"444_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2023.105732","volume":"141","author":"PC Mayer","year":"2023","unstructured":"Mayer PC, Cabral FG, Moreira MV (2023) A protocol for decentralized synchronous diagnosis with coordination. Control Eng Pract 141:105732","journal-title":"Control Eng Pract"},{"key":"444_CR22","doi-asserted-by":"crossref","unstructured":"Mayer PC, Cabral FG, Lima PM, Moreira MV (2024) Current-state opacity based on state outputs. In: 17th IFAC workshop on discrete event systems (WODES 2024) IFAC-PapersOnLine, vol. 58. Rio de Janeiro, Brazil, pp 19\u201323","DOI":"10.1016\/j.ifacol.2024.07.004"},{"key":"444_CR23","doi-asserted-by":"crossref","unstructured":"Saboori A, Hadjicostis CN (2007) Notions of security and opacity in discrete event systems. In: Proceedings of the IEEE conference on decision and control, pp 5056\u20135061","DOI":"10.1109\/CDC.2007.4434515"},{"issue":"2","key":"444_CR24","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1109\/87.486338","volume":"4","author":"M Sampath","year":"1996","unstructured":"Sampath M, Sengupta R, Lafortune S, Sinnamohideen K, Teneketzis DC (1996) Failure diagnosis using discrete-event models. IEEE Trans Control Syst Technol 4(2):105\u2013124","journal-title":"IEEE Trans Control Syst Technol"},{"key":"444_CR25","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1016\/j.automatica.2018.04.006","volume":"94","author":"R Su","year":"2018","unstructured":"Su R (2018) Supervisor synthesis to thwart cyber attack with bounded sensor reading alterations. Automatica 94:35\u201344","journal-title":"Automatica"},{"key":"444_CR26","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s10626-017-0264-7","volume":"28","author":"Y Tong","year":"2018","unstructured":"Tong Y, Li Z, Seatzu C, Giua A (2018) Current-state opacity enforcement in discrete event systems under incomparable observations. Discr Event Dyn Syst Theory Appl 28:161\u2013182","journal-title":"Discr Event Dyn Syst Theory Appl"},{"issue":"5","key":"444_CR27","doi-asserted-by":"publisher","first-page":"1336","DOI":"10.1016\/j.automatica.2014.02.038","volume":"50","author":"Y-C Wu","year":"2014","unstructured":"Wu Y-C, Lafortune S (2014) Synthesis of insertion functions for enforcement of opacity security properties. Automatica 50(5):1336\u20131348","journal-title":"Automatica"},{"key":"444_CR28","doi-asserted-by":"crossref","unstructured":"Yin X, Lafortune S (2015) A new approach for synthesizing opacity-enforcing supervisors for partially-observed discrete-event systems. In: 2015 American control conference (ACC), pp 377\u2013383","DOI":"10.1109\/ACC.2015.7170765"},{"issue":"2","key":"444_CR29","doi-asserted-by":"publisher","first-page":"614","DOI":"10.1002\/asjc.2570","volume":"24","author":"Z Zhipeng","year":"2022","unstructured":"Zhipeng Z, Xia C, Chen S (2022) Security and privacy with opacity-based state observation for finite state machine. Asian J Control 24(2):614\u2013625","journal-title":"Asian J Control"}],"container-title":["Discrete Event Dynamic Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10626-026-00444-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10626-026-00444-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10626-026-00444-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T00:31:58Z","timestamp":1782347518000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10626-026-00444-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,25]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,12]]}},"alternative-id":["444"],"URL":"https:\/\/doi.org\/10.1007\/s10626-026-00444-x","relation":{},"ISSN":["0924-6703","1573-7594"],"issn-type":[{"value":"0924-6703","type":"print"},{"value":"1573-7594","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,25]]},"assertion":[{"value":"1 November 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 June 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Financial interests"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"23"}}