{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,5]],"date-time":"2025-07-05T12:40:07Z","timestamp":1751719207637,"version":"3.41.0"},"publisher-location":"Cham","reference-count":19,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319948119"},{"type":"electronic","value":"9783319948126"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-94812-6_4","type":"book-chapter","created":{"date-parts":[[2018,6,28]],"date-time":"2018-06-28T22:12:26Z","timestamp":1530223946000},"page":"41-45","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Validity of Weighted Automata"],"prefix":"10.1007","author":[{"given":"Sylvain","family":"Lombardy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jacques","family":"Sakarovitch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,6,29]]},"reference":[{"key":"4_CR1","volume-title":"Noncommutative Rational Series with Applications","author":"J Berstel","year":"2011","unstructured":"Berstel, J., Reutenauer, C.: Noncommutative Rational Series with Applications. Cambridge University Press, Cambridge (2011)"},{"key":"4_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-78034-9","volume-title":"Iteration Theories","author":"SL Bloom","year":"1993","unstructured":"Bloom, S.L., \u00c9sik, Z.: Iteration Theories. Springer, Heidelberg (1993). https:\/\/doi.org\/10.1007\/978-3-642-78034-9"},{"key":"4_CR3","doi-asserted-by":"crossref","first-page":"19","DOI":"10.3233\/FUN-2008-861-202","volume":"86","author":"SL Bloom","year":"2008","unstructured":"Bloom, S.L., \u00c9sik, Z., Kuich, W.: Partial Conway and iteration semirings. Fundam. Inform. 86, 19\u201340 (2008)","journal-title":"Fundam. Inform."},{"key":"4_CR4","volume-title":"Regular Algebra and Finite Machines","author":"JH Conway","year":"1971","unstructured":"Conway, J.H.: Regular Algebra and Finite Machines. Chapman and Hall, London (1971)"},{"key":"4_CR5","first-page":"3","volume-title":"Monographs in Theoretical Computer Science","author":"Manfred Droste","year":"2009","unstructured":"Droste, M., Kuich, W.: Semirings and formal power series. In: Droste et al. [6], pp. 3\u201328"},{"key":"4_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01492-5","volume-title":"Handbook of Weighted Automata","year":"2009","unstructured":"Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-01492-5"},{"key":"4_CR7","volume-title":"Automata, Languages and Machines","author":"S Eilenberg","year":"1974","unstructured":"Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press, New York (1974)"},{"key":"4_CR8","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s00605-001-0481-9","volume":"137","author":"Z \u00c9sik","year":"2002","unstructured":"\u00c9sik, Z., Kuich, W.: Locally closed semirings. Monatshefte f\u00fcr Mathematik 137, 21\u201329 (2002)","journal-title":"Monatshefte f\u00fcr Mathematik"},{"key":"4_CR9","first-page":"69","volume-title":"Monographs in Theoretical Computer Science","author":"Zolt\u00e1n \u00c9sik","year":"2009","unstructured":"\u00c9sik, Z., Kuich, W.: Finite automata. In: Droste et al. [6], pp. 69\u2013104"},{"key":"4_CR10","volume-title":"Introduction to Automata Theory, Languages and Computation","author":"JE Hopcroft","year":"2006","unstructured":"Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation, 3rd edn. Addison-Wesley, Boston (2006)","edition":"3"},{"key":"4_CR11","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/0304-3975(91)90147-T","volume":"79","author":"W Kuich","year":"1991","unstructured":"Kuich, W.: Automata and languages generalized to $$\\omega $$-continuous semirings. Theoret. Comput. Sci. 79, 137\u2013150 (1991)","journal-title":"Theoret. Comput. Sci."},{"key":"4_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69959-7","volume-title":"Semirings, Automata, Languages","author":"W Kuich","year":"1986","unstructured":"Kuich, W., Salomaa, A.: Semirings, Automata, Languages. Springer, Heidelberg (1986). https:\/\/doi.org\/10.1007\/978-3-642-69959-7"},{"key":"4_CR13","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/0304-3975(77)90056-1","volume":"4","author":"DJ Lehmann","year":"1977","unstructured":"Lehmann, D.J.: Algebraic structure for transitive closure. Theoret. Comput. Sci. 4, 59\u201376 (1977)","journal-title":"Theoret. Comput. Sci."},{"issue":"4","key":"4_CR14","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1142\/S0218196713400146","volume":"23","author":"S Lombardy","year":"2013","unstructured":"Lombardy, S., Sakarovitch, J.: The validity of weighted automata. Int. J. Algebra Comput. 23(4), 863\u2013914 (2013)","journal-title":"Int. J. Algebra Comput."},{"key":"4_CR15","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1142\/S0129054102000996","volume":"13","author":"M Mohri","year":"2002","unstructured":"Mohri, M.: Generic $$\\varepsilon $$-removal and input $$\\varepsilon $$-normalization algorithms for weighted transducers. Int. J. Found. Comput. Sci. 13, 129\u2013143 (2002)","journal-title":"Int. J. Found. Comput. Sci."},{"doi-asserted-by":"crossref","unstructured":"Mohri, M.: Weighted automata algorithms. In: Droste et al. [6], pp. 213\u2013254","key":"4_CR16","DOI":"10.1007\/978-3-642-01492-5_6"},{"unstructured":"Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, Cambridge (2009). corrected English translation of \u00c9l\u00e9ments de th\u00e9orie des automates, Vuibert, Paris (2003)","key":"4_CR17"},{"key":"4_CR18","first-page":"105","volume-title":"Monographs in Theoretical Computer Science","author":"Jacques Sakarovitch","year":"2009","unstructured":"Sakarovitch, J.: Rational and recognisable power series. In: Droste et al. [6], pp. 105\u2013174"},{"unstructured":"Awali: Another Weighted Automata LIbrary. vaucanson-project.org\/AWALI","key":"4_CR19"}],"container-title":["Lecture Notes in Computer Science","Implementation and Application of Automata"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-94812-6_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,5]],"date-time":"2025-07-05T12:05:48Z","timestamp":1751717148000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-94812-6_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319948119","9783319948126"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-94812-6_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2018]]},"assertion":[{"value":"29 June 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CIAA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Implementation and Application of Automata","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Charlottetown, PE","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 July 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 August 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"wia2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.smcs.upei.ca\/ciaa2018","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}