{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T04:05:40Z","timestamp":1783051540551,"version":"3.54.6"},"publisher-location":"Cham","reference-count":39,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032262035","type":"print"},{"value":"9783032262042","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T00:00:00Z","timestamp":1779062400000},"content-version":"vor","delay-in-days":137,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Active automata learning (AAL) algorithms can learn a behavioral model of a system from interacting with it. The primary challenge remains scaling to larger models, in particular in the presence of many possible inputs to the system. Modern AAL algorithms fail to scale even if, in every state, most inputs lead to errors. In various challenging problems from the literature, these errors are observable, i.e., they emit a known error output. Motivated by these problems, we study learning these systems more efficiently. Further, we consider various degrees of knowledge about which inputs are non-error producing at which state. For each level of knowledge, we provide a matching adaptation of the state-of-the-art AAL algorithm\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$L^{\\#}$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mo>#<\/mml:mo>\n                          <\/mml:msup>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    to make the most of this domain knowledge. Our empirical evaluation demonstrates that the methods accelerate learning by orders of magnitude with strong but realistic domain knowledge to a single order of magnitude with limited domain knowledge.\n                  <\/jats:p>","DOI":"10.1007\/978-3-032-26204-2_27","type":"book-chapter","created":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T15:50:00Z","timestamp":1779033000000},"page":"520-540","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Error-Awareness Accelerates Active Automata Learning"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-3275-6806","authenticated-orcid":false,"given":"Loes","family":"Kruger","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0978-8466","authenticated-orcid":false,"given":"Sebastian","family":"Junges","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1404-6232","authenticated-orcid":false,"given":"Jurriaan","family":"Rot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,18]]},"reference":[{"issue":"2","key":"27_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0890-5401(87)90052-6","volume":"75","author":"D Angluin","year":"1987","unstructured":"Angluin, D.: Learning regular sets from queries and counterexamples. Inf. Comput. 75(2), 87\u2013106 (1987)","journal-title":"Inf. Comput."},{"key":"27_CR2","doi-asserted-by":"publisher","unstructured":"Bork, A., Chakraborty, D., Grover, K., Kret\u00ednsk\u00fd, J., Mohr, S.: Learning explainable and better performing representations of POMDP strategies. In: Finkbeiner, B., Kov\u00e1cs, L. (eds.) TACAS (2). LNCS, vol. 14571, pp. 299\u2013319. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-57249-4_15","DOI":"10.1007\/978-3-031-57249-4_15"},{"key":"27_CR3","unstructured":"Chalupar, G., Peherstorfer, S., Poll, E., de\u00a0Ruiter, J.: Automated reverse engineering using lego\u00ae. In: WOOT. USENIX Association (2014)"},{"key":"27_CR4","doi-asserted-by":"publisher","unstructured":"Damasceno, C.D.N., Mousavi, M.R., da Silva Simao, A.: Learning to Reuse: Adaptive Model Learning for Evolving Systems. In: Ahrendt, W., Tapia Tarifa, S.L. (eds.) IFM 2019. LNCS, vol. 11918, pp. 138\u2013156. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-34968-4_8","DOI":"10.1007\/978-3-030-34968-4_8"},{"key":"27_CR5","doi-asserted-by":"publisher","unstructured":"Dengler, G., Apel, S., Hermanns, H.: Automata learning - expect delays! In: Damiani, F., Farrell, M. (eds.) iFM 2025. LNCS, vol. 16194, pp. 461\u2013484. Springer, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-032-10794-7_23","DOI":"10.1007\/978-3-032-10794-7_23"},{"key":"27_CR6","doi-asserted-by":"crossref","unstructured":"Dierks, T., Rescorla, E.: The transport layer security (tls) protocol version 1.2. Technical report (2008)","DOI":"10.17487\/rfc5246"},{"key":"27_CR7","doi-asserted-by":"crossref","unstructured":"Ferreira, T., van Heerdt, G., Silva, A.: Tree-based adaptive model learning. In: A Journey from Process Algebra via Timed Automata to Model Learning. LNCS, vol. 13560, pp. 164\u2013179. Springer (2022)","DOI":"10.1007\/978-3-031-15629-8_10"},{"key":"27_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"454","DOI":"10.1007\/978-3-319-41540-6_25","volume-title":"Computer Aided Verification","author":"P Fiter\u0103u-Bro\u015ftean","year":"2016","unstructured":"Fiter\u0103u-Bro\u015ftean, P., Janssen, R., Vaandrager, F.: Combining model learning and model checking to analyze TCP implementations. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 454\u2013471. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-41540-6_25"},{"key":"27_CR9","doi-asserted-by":"crossref","unstructured":"Fiterau-Brostean, P., Lenaerts, T., Poll, E., de\u00a0Ruiter, J., Vaandrager, F.W., Verleg, P.: Model learning and model checking of SSH implementations. In: SPIN, pp. 142\u2013151. ACM (2017)","DOI":"10.1145\/3092282.3092289"},{"key":"27_CR10","doi-asserted-by":"publisher","unstructured":"Ganty, P.: Learning the state machine behind a modal text editor: The (neo)vim case study. In: Neele, T., Wijs, A. (eds.) SPIN 2024. LNCS, vol. 14624, pp. 167\u2013175. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-66149-5_9","DOI":"10.1007\/978-3-031-66149-5_9"},{"key":"27_CR11","doi-asserted-by":"crossref","unstructured":"Garhewal, B., Damasceno, C.D.N.: An experimental evaluation of conformance testing techniques in active automata learning. In: MODELS. pp. 217\u2013227. IEEE (2023)","DOI":"10.1109\/MODELS58315.2023.00012"},{"issue":"5","key":"27_CR12","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1093\/jigpal\/jzl007","volume":"14","author":"A Groce","year":"2006","unstructured":"Groce, A., Peled, D.A., Yannakakis, M.: Adaptive model checking. Log. J. IGPL 14(5), 729\u2013744 (2006)","journal-title":"Log. J. IGPL"},{"key":"27_CR13","unstructured":"Henry, L., Mousavi, M.R., Neele, T., Sammartino, M.: Compositional active learning of synchronizing systems through automated alphabet refinement. In: CONCUR. LIPIcs, vol.\u00a0348, pp. 20:1\u201320:22. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2025)"},{"key":"27_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/978-3-319-96562-8_5","volume-title":"Machine Learning for Dynamic Software Analysis: Potentials and Limits","author":"F Howar","year":"2018","unstructured":"Howar, F., Steffen, B.: Active automata learning in practice. In: Bennaceur, A., H\u00e4hnle, R., Meinke, K. (eds.) Machine Learning for Dynamic Software Analysis: Potentials and Limits. LNCS, vol. 11026, pp. 123\u2013148. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96562-8_5"},{"key":"27_CR15","doi-asserted-by":"publisher","unstructured":"Isberner, M., Howar, F., Steffen, B.: The TTT algorithm: a redundancy-free approach to active automata learning. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 307\u2013322. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-11164-3_26","DOI":"10.1007\/978-3-319-11164-3_26"},{"key":"27_CR16","doi-asserted-by":"publisher","unstructured":"Jasper, M., et al.: RERS 2019: combining synthesis with real-world models. In: Beyer, D., Huisman, M., Kordon, F., Steffen, B. (eds.) TACAS 2019. LNCS, vol. 11429, pp. 101\u2013115. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17502-3_7","DOI":"10.1007\/978-3-030-17502-3_7"},{"key":"27_CR17","doi-asserted-by":"publisher","unstructured":"Kruger, L., Junges, S., Rot, J.: Small test suites for active automata learning. In: Finkbeiner, B., Kov\u00e1cs, L. (eds.) TACAS (2). LNCS, vol. 14571, pp. 109\u2013129. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-57249-4_6","DOI":"10.1007\/978-3-031-57249-4_6"},{"key":"27_CR18","doi-asserted-by":"publisher","unstructured":"Kruger, L., Junges, S., Rot, J.: State matching and multiple references in adaptive active automata learning. In: Platzer, A., Rozier, K.Y., Pradella, M., Rossi, M. (eds.) FM 2024. LNCS, vol. 14933, pp. 267\u2013284. Springer, Cham (2024). https:\/\/doi.org\/10.1007\/978-3-031-71162-6_14","DOI":"10.1007\/978-3-031-71162-6_14"},{"key":"27_CR19","doi-asserted-by":"crossref","unstructured":"Kruger, L., Junges, S., Rot, J.: Error-awareness accelerates active automata learning (2026). https:\/\/arxiv.org\/abs\/2602.21674","DOI":"10.1007\/978-3-032-26204-2_27"},{"key":"27_CR20","doi-asserted-by":"publisher","unstructured":"Kruger, L., Junges, S., Rot, J.: Error-awareness accelerates active automata learning: supplementary material (2026). https:\/\/doi.org\/10.5281\/zenodo.18755292","DOI":"10.5281\/zenodo.18755292"},{"key":"27_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1007\/978-3-642-34026-0_39","volume-title":"Leveraging Applications of Formal Methods, Verification and Validation. Technologies for Mastering Change","author":"M Leucker","year":"2012","unstructured":"Leucker, M., Neider, D.: Learning minimal deterministic automata from inexperienced teachers. In: Margaria, T., Steffen, B. (eds.) ISoLA 2012. LNCS, vol. 7609, pp. 524\u2013538. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-34026-0_39"},{"issue":"2","key":"27_CR22","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1109\/32.265636","volume":"20","author":"G Luo","year":"1994","unstructured":"Luo, G., von Bochmann, G., Petrenko, A.: Test selection based on communicating nondeterministic finite-state machines using a generalized WP-method. IEEE Trans. Software Eng. 20(2), 149\u2013162 (1994)","journal-title":"IEEE Trans. Software Eng."},{"key":"27_CR23","doi-asserted-by":"publisher","unstructured":"van\u00a0der Maas, L., Junges, S.: Learning verified monitors for hidden markov models. In: D\u00b4Souza, M., Komondoor, R., Srivathsan, B. (eds) ATVA 2025. LNCS, vol. 16145, pp. 180\u2013203. Springer, Cham (2025). https:\/\/doi.org\/10.1007\/978-3-032-08707-2_9","DOI":"10.1007\/978-3-032-08707-2_9"},{"key":"27_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1007\/978-3-642-54862-8_41","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"O Maler","year":"2014","unstructured":"Maler, O., Mens, I.-E.: Learning regular languages over large alphabets. In: \u00c1brah\u00e1m, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 485\u2013499. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-642-54862-8_41"},{"key":"27_CR25","unstructured":"Moeller, M., Wiener, T., Solko-Breslin, A., Koch, C., Foster, N., Silva, A.: Automata learning with an incomplete teacher. In: ECOOP. LIPIcs, vol.\u00a0263, pp. 21:1\u201321:30. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2023)"},{"key":"27_CR26","first-page":"129","volume":"34","author":"EF Moore","year":"1956","unstructured":"Moore, E.F., et al.: Gedanken-experiments on sequential machines. Autom. Stud. 34, 129\u2013153 (1956)","journal-title":"Autom. Stud."},{"issue":"3","key":"27_CR27","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1007\/s11334-022-00449-3","volume":"18","author":"E Muskardin","year":"2022","unstructured":"Muskardin, E., Aichernig, B.K., Pill, I., Pferscher, A., Tappler, M.: AALpy: an active automata learning library. Innov. Syst. Softw. Eng. 18(3), 417\u2013426 (2022)","journal-title":"Innov. Syst. Softw. Eng."},{"key":"27_CR28","doi-asserted-by":"crossref","unstructured":"Muskardin, E., Burgstaller, T., Tappler, M., Aichernig, B.K.: Active model learning of git version control system. In: ICSTW. pp. 78\u201382. IEEE (2024)","DOI":"10.1109\/ICSTW60967.2024.00024"},{"key":"27_CR29","unstructured":"Petrenko, A., Yevtushenko, N., Lebedev, A., Das, A.: Nondeterministic state machines in protocol conformance testing. In: Protocol Test Systems. IFIP Transactions, vol.\u00a0C-19, pp. 363\u2013378. North-Holland (1993)"},{"key":"27_CR30","doi-asserted-by":"crossref","unstructured":"Raffelt, H., Steffen, B., Berg, T.: Learnlib: a library for automata learning and experimentation. In: FMICS, pp. 62\u201371. ACM (2005)","DOI":"10.1145\/1081180.1081189"},{"key":"27_CR31","unstructured":"de\u00a0Ruiter, J., Poll, E.: Protocol state fuzzing of TLS implementations. In: USENIX Security Symposium, pp. 193\u2013206. USENIX Association (2015)"},{"key":"27_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/978-3-319-33693-0_20","volume-title":"Integrated Formal Methods","author":"M Schuts","year":"2016","unstructured":"Schuts, M., Hooman, J., Vaandrager, F.: Refactoring of legacy software using model learning and equivalence checking: an industrial experience report. In: \u00c1brah\u00e1m, E., Huisman, M. (eds.) IFM 2016. LNCS, vol. 9681, pp. 311\u2013325. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-33693-0_20"},{"key":"27_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/978-3-319-25423-4_5","volume-title":"Formal Methods and Software Engineering","author":"W Smeenk","year":"2015","unstructured":"Smeenk, W., Moerman, J., Vaandrager, F., Jansen, D.N.: Applying automata learning to embedded control software. In: Butler, M., Conchon, S., Za\u00efdi, F. (eds.) ICFEM 2015. LNCS, vol. 9407, pp. 67\u201383. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-25423-4_5"},{"issue":"2","key":"27_CR34","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1145\/2967606","volume":"60","author":"FW Vaandrager","year":"2017","unstructured":"Vaandrager, F.W.: Model learning. Commun. ACM 60(2), 86\u201395 (2017)","journal-title":"Commun. ACM"},{"key":"27_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/978-3-030-99524-9_12","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"F Vaandrager","year":"2022","unstructured":"Vaandrager, F., Garhewal, B., Rot, J., Wi\u00dfmann, T.: A new approach for active automata learning based on apartness. In: TACAS 2022. LNCS, vol. 13243, pp. 223\u2013243. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-99524-9_12"},{"key":"27_CR36","unstructured":"Vaandrager, F.W., Melse, I.: New fault domains for conformance testing of finite state machines. In: CONCUR. LIPIcs, vol.\u00a0348, pp. 34:1\u201334:22. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2025)"},{"key":"27_CR37","doi-asserted-by":"crossref","unstructured":"Wallner, F., Aichernig, B.K., Lorber, F., Tappler, M.: Mutating skeletons: learning timed automata via domain knowledge. In: ICSTW, pp. 67\u201377. IEEE (2025)","DOI":"10.1109\/ICSTW64639.2025.10962513"},{"key":"27_CR38","doi-asserted-by":"crossref","unstructured":"Yaacov, T., Weiss, G., Amram, G., Hayoun, A.: Automata models for effective bug pattern description. In: MODELS, pp. 119\u2013129. IEEE (2025)","DOI":"10.1109\/MODELS67397.2025.00017"},{"key":"27_CR39","doi-asserted-by":"crossref","unstructured":"Yang, N., et al.: Improving model inference in industry by combining active and passive learning. In: SANER, pp. 253\u2013263. IEEE (2019)","DOI":"10.1109\/SANER.2019.8668007"}],"container-title":["Lecture Notes in Computer Science","Formal Methods"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-26204-2_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T17:58:41Z","timestamp":1783015121000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-26204-2_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032262035","9783032262042"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-26204-2_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"18 May 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"FM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Formal Methods","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Tokyo","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Japan","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 May 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 May 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"fm2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/conf.researchr.org\/home\/fm-2026","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}