{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:15:39Z","timestamp":1759637739340,"version":"3.40.3"},"publisher-location":"Cham","reference-count":19,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030625351"},{"type":"electronic","value":"9783030625368"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-62536-8_6","type":"book-chapter","created":{"date-parts":[[2020,11,7]],"date-time":"2020-11-07T02:02:50Z","timestamp":1604714570000},"page":"64-77","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["State Complexity Bounds for the Commutative Closure of Group Languages"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7866-075X","authenticated-orcid":false,"given":"Stefan","family":"Hoffmann","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,11,6]]},"reference":[{"key":"6_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/978-3-319-41114-9_6","volume-title":"Descriptional Complexity of Formal Systems","author":"J Brzozowski","year":"2016","unstructured":"Brzozowski, J., Jir\u00e1skov\u00e1, G., Liu, B., Rajasekaran, A., Szyku\u0142a, M.: On the state complexity of the shuffle of regular languages. In: C\u00e2mpeanu, C., Manea, F., Shallit, J. (eds.) DCFS 2016. LNCS, vol. 9777, pp. 73\u201386. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-41114-9_6"},{"key":"6_CR2","series-title":"London Mathematical Society Student Texts","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623677","volume-title":"Permutation Groups","author":"PJ Cameron","year":"1999","unstructured":"Cameron, P.J.: Permutation Groups. London Mathematical Society Student Texts. Cambridge University Press, Cambridge (1999)"},{"key":"6_CR3","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.tcs.2017.03.007","volume":"682","author":"D Cho","year":"2017","unstructured":"Cho, D., Goc, D., Han, Y., Ko, S., Palioudakis, A., Salomaa, K.: State complexity of permutation on finite languages over a binary alphabet. Theor. Comput. Sci. 682, 67\u201378 (2017)","journal-title":"Theor. Comput. Sci."},{"key":"6_CR4","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1016\/0304-3975(82)90124-4","volume":"27","author":"A Ehrenfeucht","year":"1983","unstructured":"Ehrenfeucht, A., Haussler, D., Rozenberg, G.: On regularity of context-free languages. Theor. Comput. Sci. 27, 311\u2013332 (1983)","journal-title":"Theor. Comput. Sci."},{"issue":"4","key":"6_CR5","first-page":"251","volume":"21","author":"Y Gao","year":"2017","unstructured":"Gao, Y., Moreira, N., Reis, R., Yu, S.: A survey on operational state complexity. J. Automata Lang. Comb. 21(4), 251\u2013310 (2017)","journal-title":"J. Automata Lang. Comb."},{"key":"6_CR6","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.ic.2013.07.003","volume":"230","author":"AC G\u00f3mez","year":"2013","unstructured":"G\u00f3mez, A.C., Guaiana, G., Pin, J.: Regular languages and partial commutations. Inf. Comput. 230, 76\u201396 (2013)","journal-title":"Inf. Comput."},{"key":"6_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/978-3-540-73208-2_22","volume-title":"Developments in Language Theory","author":"Y-S Han","year":"2007","unstructured":"Han, Y.-S., Salomaa, K.: State complexity of union and intersection of finite languages. In: Harju, T., Karhum\u00e4ki, J., Lepist\u00f6, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 217\u2013228. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-73208-2_22"},{"issue":"3","key":"6_CR8","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1142\/S0129054108005838","volume":"19","author":"Y Han","year":"2008","unstructured":"Han, Y., Salomaa, K.: State complexity of union and intersection of finite languages. Int. J. Found. Comput. Sci. 19(3), 581\u2013595 (2008)","journal-title":"Int. J. Found. Comput. Sci."},{"key":"6_CR9","unstructured":"Hoffmann, S.: State complexity, properties and generalizations of commutative regular languages. Inf. Comput. (submitted)"},{"key":"6_CR10","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/978-3-030-21363-3_13","volume-title":"CAI 2019","author":"S Hoffmann","year":"2019","unstructured":"Hoffmann, S.: Commutative regular languages - properties and state complexity. In: \u0106iri\u0107, M., Droste, M., Pin, J.\u00c9. (eds.) CAI 2019. LNCS, vol. 11545, pp. 151\u2013163. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-21363-3_13"},{"key":"6_CR11","unstructured":"Hoffmann, S.: State complexity of permutation on finite languages. CoRR abs\/2006.15178 (2020). https:\/\/arxiv.org\/abs\/2006.15178"},{"key":"6_CR12","doi-asserted-by":"crossref","unstructured":"Holzer, M., Kutrib, M.: Descriptional complexity - an introductory survey. In: Mart\u00edn-Vide, C. (ed.) Scientific Applications of Language Methods, Mathematics, Computing, Language, and Life: Frontiers in Mathematical Linguistics and Language Theory, vol. 2, pp. 1\u201358. World Scientific\/Imperial College Press (2010)","DOI":"10.1142\/9781848165458_0001"},{"issue":"3","key":"6_CR13","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1016\/j.ic.2010.11.013","volume":"209","author":"M Holzer","year":"2011","unstructured":"Holzer, M., Kutrib, M.: Descriptional and computational complexity of finite automata - a survey. Inf. Comput. 209(3), 456\u2013470 (2011)","journal-title":"Inf. Comput."},{"key":"6_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1007\/978-3-030-48516-0_10","volume-title":"Developments in Language Theory","author":"M Hospod\u00e1r","year":"2020","unstructured":"Hospod\u00e1r, M., Mlyn\u00e1r\u010dik, P.: Operations on permutation automata. In: Jonoska, N., Savchuk, D. (eds.) DLT 2020. LNCS, vol. 12086, pp. 122\u2013136. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-48516-0_10"},{"issue":"6","key":"6_CR15","first-page":"1266","volume":"194","author":"AN Maslov","year":"1970","unstructured":"Maslov, A.N.: Estimates of the number of states of finite automata. Dokl. Akad. Nauk SSSR 194(6), 1266\u20131268 (1970)","journal-title":"Dokl. Akad. Nauk SSSR"},{"issue":"1","key":"6_CR16","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1017\/S135132499600126X","volume":"2","author":"M Mohri","year":"1996","unstructured":"Mohri, M.: On some applications of finite-state automata theory to natural language processing. Nat. Lang. Eng. 2(1), 61\u201380 (1996)","journal-title":"Nat. Lang. Eng."},{"key":"6_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1007\/978-3-319-19225-3_19","volume-title":"Descriptional Complexity of Formal Systems","author":"A Palioudakis","year":"2015","unstructured":"Palioudakis, A., Cho, D.-J., Go\u010d, D., Han, Y.-S., Ko, S.-K., Salomaa, K.: The state complexity of permutations on finite languages over binary alphabets. In: Shallit, J., Okhotin, A. (eds.) DCFS 2015. LNCS, vol. 9118, pp. 220\u2013230. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-19225-3_19"},{"volume-title":"Handbook of Finite State Based Models and Applications","year":"2012","key":"6_CR18","unstructured":"Wang, J. (ed.): Handbook of Finite State Based Models and Applications. Chapman and Hall\/CRC, Boca Raton (2012)"},{"issue":"2","key":"6_CR19","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0304-3975(92)00011-F","volume":"125","author":"S Yu","year":"1994","unstructured":"Yu, S., Zhuang, Q., Salomaa, K.: The state complexities of some basic operations on regular languages. Theor. Comput. Sci. 125(2), 315\u2013328 (1994)","journal-title":"Theor. Comput. Sci."}],"container-title":["Lecture Notes in Computer Science","Descriptional Complexity of Formal Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-62536-8_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T19:22:50Z","timestamp":1741634570000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-62536-8_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030625351","9783030625368"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-62536-8_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"6 November 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"DCFS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Descriptional Complexity of Formal Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Vienna","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Austria","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 August 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 August 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"dcfs2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/sofl2020.conf.tuwien.ac.at\/DCFS2020\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}