{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T08:03:13Z","timestamp":1784793793217,"version":"3.55.0"},"publisher-location":"Cham","reference-count":51,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032325181","type":"print"},{"value":"9783032325198","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":[[2026,7,24]],"date-time":"2026-07-24T00:00:00Z","timestamp":1784851200000},"content-version":"vor","delay-in-days":204,"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                    We present\n                    <jats:sc>Kofola<\/jats:sc>\n                    , an efficient tool for complementation and inclusion checking of B\u00fcchi automata, two central tasks in automata-theoretic verification with applications in model checking, monitoring, and theorem proving.\n                    <jats:sc>Kofola<\/jats:sc>\n                    implements a state-of-the-art modular complementation framework that decomposes the input automaton into strongly connected components and applies to each component a complementation algorithm tailored to its structural properties. Building on this modular construction,\n                    <jats:sc>Kofola<\/jats:sc>\n                    also provides modular\n                    <jats:italic>inclusion checking<\/jats:italic>\n                    with new heuristics. A key ingredient is a\u00a0new on-the-fly emptiness-checking algorithm for the simple generalized Rabin\u00a0pair condition produced by our complementation, allowing the search to terminate\u00a0as soon as the explored state space suffices. Empirical evaluation shows that\n                    <jats:sc>Kofola<\/jats:sc>\n                    \u00a0is highly competitive with state-of-the-art complementation and inclusion-checking tools: it is the most robust tool in our evaluation and often outperforms competitors by several orders of magnitude on benchmarks from practical applications.\n                  <\/jats:p>","DOI":"10.1007\/978-3-032-32519-8_10","type":"book-chapter","created":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T07:18:07Z","timestamp":1784791087000},"page":"181-197","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Kofola 1.0: A Modular Approach to $$\\omega $$-Regular Complementation and\u00a0Inclusion Checking"],"prefix":"10.1007","author":[{"given":"Ondrej","family":"Alexaj","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vojt\u011bch","family":"Havlena","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luk\u00e1\u0161","family":"Hol\u00edk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ond\u0159ej","family":"Leng\u00e1l","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nicolas","family":"Mazzocchi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,24]]},"reference":[{"key":"10_CR1","unstructured":"Automata-benchmarks (2025). https:\/\/github.com\/ondrik\/automata-benchmarks\/tree\/master\/omega\/"},{"key":"10_CR2","unstructured":"Kofola (2025). https:\/\/github.com\/VeriFIT\/kofola"},{"key":"10_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1007\/978-3-642-14295-6_14","volume-title":"Computer Aided Verification","author":"PA Abdulla","year":"2010","unstructured":"Abdulla, P.A., et al.: Simulation subsumption in Ramsey-based B\u00fcchi automata universality and inclusion testing. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 132\u2013147. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-14295-6_14"},{"key":"10_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/978-3-642-23217-6_13","volume-title":"CONCUR 2011 \u2013 Concurrency Theory","author":"PA Abdulla","year":"2011","unstructured":"Abdulla, P.A., et al.: Advanced Ramsey-based B\u00fcchi automata inclusion testing. In: Katoen, J.-P., K\u00f6nig, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 187\u2013202. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-23217-6_13"},{"key":"10_CR5","doi-asserted-by":"publisher","unstructured":"Alexaj, O., Havlena, V., Hol\u00edk, L., Leng\u00e1l, O., Li, Y., Mazzocchi, N.: Artifact: Kofola 1.0: a modular approach to $$\\omega $$-regular complementation and inclusion checking (2025). https:\/\/doi.org\/10.5281\/zenodo.17478623","DOI":"10.5281\/zenodo.17478623"},{"key":"10_CR6","unstructured":"Alexaj, O., Havlena, V., Hol\u00edk, L., Leng\u00e1l, O., Li, Y., Mazzocchi, N.: Kofola 1.0: a\u00a0modular approach to $$\\omega $$-regular complementation and inclusion checking (technical report). CoRR abs\/2605.15390 (2026). http:\/\/arxiv.org\/abs\/2605.15390"},{"key":"10_CR7","doi-asserted-by":"publisher","unstructured":"Allred, J.D., Ultes-Nitsche, U.: A simple and optimal complementation algorithm for B\u00fcchi automata. In: Dawar, A., Gr\u00e4del, E. (eds.) Proceedings of the 33rd Annual ACM\/IEEE Symposium on Logic in Computer Science, LICS 2018, Oxford, UK, July 09-12, 2018, pp. 46\u201355. ACM (2018). https:\/\/doi.org\/10.1145\/3209108.3209138","DOI":"10.1145\/3209108.3209138"},{"key":"10_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/978-3-319-21690-4_31","volume-title":"Computer Aided Verification","author":"T Babiak","year":"2015","unstructured":"Babiak, T., et al.: The hanoi omega-automata format. In: Kroening, D., P\u0103s\u0103reanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 479\u2013486. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-21690-4_31"},{"key":"10_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/978-3-030-31784-3_26","volume-title":"Automated Technology for Verification and Analysis","author":"C Baier","year":"2019","unstructured":"Baier, C., Blahoudek, F., Duret-Lutz, A., Klein, J., M\u00fcller, D., Strej\u010dek, J.: Generic emptiness check for fun and profit. In: Chen, Y.-F., Cheng, C.-H., Esparza, J. (eds.) ATVA 2019. LNCS, vol. 11781, pp. 445\u2013461. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-31784-3_26"},{"key":"10_CR10","doi-asserted-by":"publisher","unstructured":"Beutner, R., Finkbeiner, B.: AutoHyper: explicit-state model checking for HyperLTL. In: Sankaranarayanan, S., Sharygina, N. (eds.) Tools and Algorithms for the Construction and Analysis of Systems - 29th International Conference, TACAS 2023, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022, Paris, France, April 22-27, 2023, Proceedings, Part I. LNCS, vol. 13993, pp. 145\u2013163. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-30823-9_8","DOI":"10.1007\/978-3-031-30823-9_8"},{"key":"10_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/978-3-030-53291-8_2","volume-title":"Computer Aided Verification","author":"F Blahoudek","year":"2020","unstructured":"Blahoudek, F., Duret-Lutz, A., Strej\u010dek, J.: Seminator 2 can complement generalized B\u00fcchi automata via improved semi-determinization. In: Lahiri, S.K., Wang, C. (eds.) CAV 2020. LNCS, vol. 12225, pp. 15\u201327. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-53291-8_2"},{"key":"10_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/978-3-642-28729-9_10","volume-title":"Foundations of Software Science and Computational Structures","author":"S Breuers","year":"2012","unstructured":"Breuers, S., L\u00f6ding, C., Olschewski, J.: Improved Ramsey-based B\u00fcchi complementation. In: Birkedal, L. (ed.) FoSSaCS 2012. LNCS, vol. 7213, pp. 150\u2013164. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-28729-9_10"},{"key":"10_CR13","unstructured":"B\u00fcchi, J.R.: On a decision method in restricted second order arithmetic, logic, methodology and philosophy of science (proc. 1960 internat. congr.) (1962)"},{"key":"10_CR14","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/10721959_20","volume-title":"Automated Deduction - CADE-17","author":"D Bustan","year":"2000","unstructured":"Bustan, D., Grumberg, O.: Simulation based minimization. In: McAllester, D. (ed.) CADE 2000. LNCS (LNAI), vol. 1831, pp. 255\u2013270. Springer, Heidelberg (2000). https:\/\/doi.org\/10.1007\/10721959_20"},{"key":"10_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"447","DOI":"10.1007\/978-3-030-34175-6_23","volume-title":"Programming Languages and Systems","author":"Y-F Chen","year":"2019","unstructured":"Chen, Y.-F., Havlena, V., Leng\u00e1l, O.: Simulations in rank-based B\u00fcchi automata complementation. In: Lin, A.W. (ed.) APLAS 2019. LNCS, vol. 11893, pp. 447\u2013467. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-34175-6_23"},{"key":"10_CR16","doi-asserted-by":"publisher","unstructured":"Chen, Y., et al.: Advanced automata-based algorithms for program termination checking. In: Foster, J.S., Grossman, D. (eds.) Proceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2018, Philadelphia, PA, USA, June 18-22, 2018, pp. 135\u2013150. ACM (2018). https:\/\/doi.org\/10.1145\/3192366.3192405","DOI":"10.1145\/3192366.3192405"},{"key":"10_CR17","doi-asserted-by":"publisher","unstructured":"Clemente, L., Mayr, R.: Efficient reduction of nondeterministic automata with application to language inclusion testing. Log. Methods Comput. Sci. 15(1) (2019). https:\/\/doi.org\/10.23638\/LMCS-15(1:12)2019","DOI":"10.23638\/LMCS-15(1:12)2019"},{"key":"10_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/3-540-48119-2_16","volume-title":"FM\u201999 \u2014 Formal Methods","author":"J-M Couvreur","year":"1999","unstructured":"Couvreur, J.-M.: On-the-fly verification of linear temporal logic. In: Wing, J.M., Woodcock, J., Davies, J. (eds.) FM 1999. LNCS, vol. 1708, pp. 253\u2013271. Springer, Heidelberg (1999). https:\/\/doi.org\/10.1007\/3-540-48119-2_16"},{"key":"10_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/978-3-319-25150-9_3","volume-title":"Theoretical Aspects of Computing - ICTAC 2015","author":"V Diekert","year":"2015","unstructured":"Diekert, V., Muscholl, A., Walukiewicz, I.: A note on monitors and B\u00fcchi automata. In: Leucker, M., Rueda, C., Valencia, F.D. (eds.) ICTAC 2015. LNCS, vol. 9399, pp. 39\u201357. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-25150-9_3"},{"key":"10_CR20","doi-asserted-by":"publisher","unstructured":"Doveri, K., Ganty, P., Mazzocchi, N.: FORQ-based language inclusion formal testing. In: Shoham, S., Vizel, Y. (eds.) Computer Aided Verification - 34th International Conference, CAV 2022, Haifa, Israel, August 7-10, 2022, Proceedings, Part II. Lecture Notes in Computer Science, vol. 13372, pp. 109\u2013129. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-13188-2_6","DOI":"10.1007\/978-3-031-13188-2_6"},{"key":"10_CR21","doi-asserted-by":"publisher","unstructured":"Doveri, K., Ganty, P., Ranzato, F.: Inclusion testing of B\u00fcchi automata based on well-quasiorders. In: Haddad, S., Varacca, D. (eds.) 32nd International Conference on Concurrency Theory, CONCUR 2021, August 24-27, 2021, Virtual Conference. LIPIcs, vol.\u00a0203, pp. 3:1\u20133:22. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2021). https:\/\/doi.org\/10.4230\/LIPICS.CONCUR.2021.3","DOI":"10.4230\/LIPICS.CONCUR.2021.3"},{"key":"10_CR22","doi-asserted-by":"publisher","unstructured":"Duret-Lutz, A., et al.: From Spot\u00a02.0 to Spot\u00a02.10: what\u2019s new? In: Shoham, S., Vizel, Y. (eds.) Computer Aided Verification - 34th International Conference, CAV 2022, Haifa, Israel, August 7-10, 2022, Proceedings, Part II. LNCS, vol. 13372, pp. 174\u2013187. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-13188-2_9","DOI":"10.1007\/978-3-031-13188-2_9"},{"issue":"3","key":"10_CR23","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/0167-6423(87)90036-0","volume":"8","author":"EA Emerson","year":"1987","unstructured":"Emerson, E.A., Lei, C.: Modalities for model checking: branching time logic strikes back. Sci. Comput. Program. 8(3), 275\u2013306 (1987). https:\/\/doi.org\/10.1016\/0167-6423(87)90036-0","journal-title":"Sci. Comput. Program."},{"key":"10_CR24","unstructured":"Esparza, J., Blondin, M.: Automata Theory: An Algorithmic Approach, MIT Press (2023)"},{"issue":"4","key":"10_CR25","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1142\/S0129054106004145","volume":"17","author":"E Friedgut","year":"2006","unstructured":"Friedgut, E., Kupferman, O., Vardi, M.Y.: B\u00fcchi complementation made tighter. Int. J. Found. Comput. Sci. 17(4), 851\u2013868 (2006). https:\/\/doi.org\/10.1142\/S0129054106004145","journal-title":"Int. J. Found. Comput. Sci."},{"key":"10_CR26","doi-asserted-by":"publisher","unstructured":"Havlena, V., Leng\u00e1l, O., Li, Y., \u0160mahl\u00edkov\u00e1, B., Turrini, A.: Modular mix-and-match complementation of B\u00fcchi automata. In: Sankaranarayanan, S., Sharygina, N. (eds.) Tools and Algorithms for the Construction and Analysis of Systems, pp. 249\u2013270. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-30823-9_13","DOI":"10.1007\/978-3-031-30823-9_13"},{"key":"10_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1007\/978-3-030-91014-3_15","volume-title":"Networked Systems","author":"V Havlena","year":"2021","unstructured":"Havlena, V., Leng\u00e1l, O., \u0160mahl\u00edkov\u00e1, B.: Deciding S1S: down the rabbit hole and through the looking glass. In: Echihabi, K., Meyer, R. (eds.) NETYS 2021. LNCS, vol. 12754, pp. 215\u2013222. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-91014-3_15"},{"key":"10_CR28","doi-asserted-by":"publisher","unstructured":"Havlena, V., Leng\u00e1l, O.: Reducing (to) the ranks: efficient rank-based B\u00fcchi automata complementation. In: Haddad, S., Varacca, D. (eds.) 32nd International Conference on Concurrency Theory, CONCUR 2021, August 24-27, 2021, Virtual Conference. LIPIcs, vol.\u00a0203, pp. 2:1\u20132:19. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2021). https:\/\/doi.org\/10.4230\/LIPIcs.CONCUR.2021.2","DOI":"10.4230\/LIPIcs.CONCUR.2021.2"},{"key":"10_CR29","doi-asserted-by":"publisher","unstructured":"Havlena, V., Leng\u00e1l, O., \u0160mahl\u00edkov\u00e1, B.: Complementing B\u00fcchi automata with ranker. In: Shoham, S., Vizel, Y. (eds.) Computer Aided Verification - 34th International Conference, CAV 2022, Haifa, Israel, August 7-10, 2022, Proceedings, Part II. LNCS, vol. 13372, pp. 188\u2013201. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-13188-2_10","DOI":"10.1007\/978-3-031-13188-2_10"},{"key":"10_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1007\/978-3-030-99527-0_7","volume-title":"Tools and Algorithms for the Construction and Analysis of Systems","author":"V Havlena","year":"2022","unstructured":"Havlena, V., Leng\u00e1l, O., \u0160mahl\u00edkov\u00e1, B.: Sky is not the limit. In: Fisman, D., Rosu, G. (eds.) TACAS 2022. LNCS, vol. 13244, pp. 118\u2013136. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-99527-0_7"},{"key":"10_CR31","doi-asserted-by":"publisher","unstructured":"Hieronymi, P., Ma, D., Oei, R., Schaeffer, L., Schulz, C., Shallit, J.O.: Decidability for Sturmian words. Log. Methods Comput. Sci. 20(3) (2024). https:\/\/doi.org\/10.46298\/LMCS-20(3:12)2024","DOI":"10.46298\/LMCS-20(3:12)2024"},{"key":"10_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"724","DOI":"10.1007\/978-3-540-70575-8_59","volume-title":"Automata, Languages and Programming","author":"D K\u00e4hler","year":"2008","unstructured":"K\u00e4hler, D., Wilke, T.: Complementation, disambiguation, and determinization of B\u00fcchi automata unified. In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5125, pp. 724\u2013735. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-70575-8_59"},{"key":"10_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1007\/978-3-642-04761-9_18","volume-title":"Automated Technology for Verification and Analysis","author":"H Karmarkar","year":"2009","unstructured":"Karmarkar, H., Chakraborty, S.: On minimal odd rankings for B\u00fcchi complementation. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 228\u2013243. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-04761-9_18"},{"key":"10_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"543","DOI":"10.1007\/978-3-030-01090-4_34","volume-title":"Automated Technology for Verification and Analysis","author":"J K\u0159et\u00ednsk\u00fd","year":"2018","unstructured":"K\u0159et\u00ednsk\u00fd, J., Meggendorfer, T., Sickert, S.: Owl: a library for $$\\omega $$-words, automata, and LTL. In: Lahiri, S.K., Wang, C. (eds.) ATVA 2018. LNCS, vol. 11138, pp. 543\u2013550. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-01090-4_34"},{"key":"10_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1007\/3-540-61474-5_84","volume-title":"Computer Aided Verification","author":"O Kupferman","year":"1996","unstructured":"Kupferman, O., Vardi, M.Y.: Verification of fair transition systems. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 372\u2013382. Springer, Heidelberg (1996). https:\/\/doi.org\/10.1007\/3-540-61474-5_84"},{"issue":"3","key":"10_CR36","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1145\/377978.377993","volume":"2","author":"O Kupferman","year":"2001","unstructured":"Kupferman, O., Vardi, M.Y.: Weak alternating automata are not that weak. ACM Trans. Comput. Log. 2(3), 408\u2013429 (2001). https:\/\/doi.org\/10.1145\/377978.377993","journal-title":"ACM Trans. Comput. Log."},{"key":"10_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/978-3-030-90870-6_25","volume-title":"Formal Methods","author":"Y Li","year":"2021","unstructured":"Li, Y., Tsay, Y.-K., Turrini, A., Vardi, M.Y., Zhang, L.: Congruence relations for B\u00fcchi automata. In: Huisman, M., P\u0103s\u0103reanu, C., Zhan, N. (eds.) FM 2021. LNCS, vol. 13047, pp. 465\u2013482. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-90870-6_25"},{"key":"10_CR38","doi-asserted-by":"publisher","unstructured":"Li, Y., Turrini, A., Feng, W., Vardi, M.Y., Zhang, L.: Divide-and-conquer determinization of B\u00fcchi automata based on SCC decomposition. In: Shoham, S., Vizel, Y. (eds.) Computer Aided Verification - 34th International Conference, CAV 2022, Haifa, Israel, August 7-10, 2022, Proceedings, Part II. Lecture Notes in Computer Science, vol. 13372, pp. 152\u2013173. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-13188-2_8","DOI":"10.1007\/978-3-031-13188-2_8"},{"key":"10_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/978-3-319-73721-8_15","volume-title":"Verification, Model Checking, and Abstract Interpretation","author":"Y Li","year":"2018","unstructured":"Li, Y., Turrini, A., Zhang, L., Schewe, S.: Learning to complement B\u00fcchi automata. In: VMCAI 2018. LNCS, vol. 10747, pp. 313\u2013335. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-73721-8_15"},{"key":"10_CR40","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1007\/978-3-030-31784-3_18","volume-title":"Automated Technology for Verification and Analysis","author":"C L\u00f6ding","year":"2019","unstructured":"L\u00f6ding, C., Pirogov, A.: New optimizations and heuristics for determinization of B\u00fcchi automata. In: Chen, Y.-F., Cheng, C.-H., Esparza, J. (eds.) ATVA 2019. LNCS, vol. 11781, pp. 317\u2013333. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-31784-3_18"},{"key":"10_CR41","doi-asserted-by":"publisher","unstructured":"Miyano, S., Hayashi, T.: Alternating finite automata on $$\\omega $$-words. Theoret. Comput. Sci. 32(3), 321\u2013330 (1984). https:\/\/doi.org\/10.1016\/0304-3975(84)90049-5","DOI":"10.1016\/0304-3975(84)90049-5"},{"key":"10_CR42","unstructured":"Oei, R., Ma, D., Schulz, C., Hieronymi, P.: Pecan: an automated theorem prover for automatic sequences using B\u00fcchi automata. CoRR abs\/2102.01727 (2021). https:\/\/arxiv.org\/abs\/2102.01727"},{"key":"10_CR43","doi-asserted-by":"publisher","unstructured":"Piterman, N.: From nondeterministic B\u00fcchi and Streett automata to deterministic parity automata. Log. Methods Comput. Sci. 3(3) (2007). https:\/\/doi.org\/10.2168\/LMCS-3(3:5)2007","DOI":"10.2168\/LMCS-3(3:5)2007"},{"key":"10_CR44","doi-asserted-by":"publisher","unstructured":"Redziejowski, R.R.: An improved construction of deterministic omega-automaton using derivatives. Fundam. Informaticae 119(3\u20134), 393\u2013406 (2012). https:\/\/doi.org\/10.3233\/FI-2012-744","DOI":"10.3233\/FI-2012-744"},{"key":"10_CR45","doi-asserted-by":"publisher","unstructured":"Safra, S.: On the complexity of omega-automata. In: 29th Annual Symposium on Foundations of Computer Science, White Plains, New York, USA, 24-26 October 1988, pp. 319\u2013327. IEEE Computer Society (1988). https:\/\/doi.org\/10.1109\/SFCS.1988.21948","DOI":"10.1109\/SFCS.1988.21948"},{"key":"10_CR46","doi-asserted-by":"publisher","unstructured":"Schewe, S.: B\u00fcchi complementation made tight. In: Albers, S., Marion, J. (eds.) 26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009, February 26-28, 2009, Freiburg, Germany, Proceedings. LIPIcs, vol.\u00a03, pp. 661\u2013672. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik, Germany (2009). https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2009.1854","DOI":"10.4230\/LIPIcs.STACS.2009.1854"},{"key":"10_CR47","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1007\/978-3-319-41540-6_17","volume-title":"Computer Aided Verification","author":"S Sickert","year":"2016","unstructured":"Sickert, S., Esparza, J., Jaax, S., K\u0159et\u00ednsk\u00fd, J.: Limit-deterministic B\u00fcchi automata for linear temporal logic. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9780, pp. 312\u2013332. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-41540-6_17"},{"key":"10_CR48","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/0304-3975(87)90008-9","volume":"49","author":"AP Sistla","year":"1987","unstructured":"Sistla, A.P., Vardi, M.Y., Wolper, P.: The complementation problem for B\u00fcchi automata with applications to temporal logic. Theor. Comput. Sci. 49, 217\u2013237 (1987). https:\/\/doi.org\/10.1016\/0304-3975(87)90008-9","journal-title":"Theor. Comput. Sci."},{"key":"10_CR49","doi-asserted-by":"publisher","unstructured":"Tarjan, R.: Depth-first search and linear graph algorithms. In: 12th Annual Symposium on Switching and Automata Theory (swat 1971), pp. 114\u2013121 (1971). https:\/\/doi.org\/10.1109\/SWAT.1971.10","DOI":"10.1109\/SWAT.1971.10"},{"key":"10_CR50","doi-asserted-by":"publisher","unstructured":"Tsai, M., Fogarty, S., Vardi, M.Y., Tsay, Y.: State of B\u00fcchi complementation. Log. Methods Comput. Sci. 10(4) (2014). https:\/\/doi.org\/10.2168\/LMCS-10(4:13)2014","DOI":"10.2168\/LMCS-10(4:13)2014"},{"key":"10_CR51","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1007\/978-3-642-01702-5_2","volume-title":"Hardware and Software: Verification and Testing","author":"MY Vardi","year":"2009","unstructured":"Vardi, M.Y.: Automata-theoretic model checking revisited. In: Chockler, H., Hu, A.J. (eds.) HVC 2008. LNCS, vol. 5394, pp. 2\u20132. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-01702-5_2"}],"container-title":["Lecture Notes in Computer Science","Computer Aided Verification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-32519-8_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T07:18:09Z","timestamp":1784791089000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-32519-8_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032325181","9783032325198"],"references-count":51,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-32519-8_10","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":"24 July 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests.","order":1,"name":"Ethics","label":"Disclosure of Interests","group":{"name":"EthicsHeading","label":"Ethics"}},{"value":"CAV","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computer Aided Verification","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Lisbon","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","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":"26 July 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 July 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"38","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cav2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.floc26.org\/program","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}