{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T07:00:55Z","timestamp":1777618855195,"version":"3.51.4"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,10,28]],"date-time":"2010-10-28T00:00:00Z","timestamp":1288224000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory Comput Syst"],"published-print":{"date-parts":[[2012,2]]},"DOI":"10.1007\/s00224-010-9296-1","type":"journal-article","created":{"date-parts":[[2010,10,27]],"date-time":"2010-10-27T07:41:39Z","timestamp":1288165299000},"page":"241-278","source":"Crossref","is-referenced-by-count":14,"title":["A B\u00fcchi-Like Theorem for Weighted Tree Automata over Multioperator Monoids"],"prefix":"10.1007","volume":"50","author":[{"given":"Zolt\u00e1n","family":"F\u00fcl\u00f6p","sequence":"first","affiliation":[]},{"given":"Torsten","family":"St\u00fcber","sequence":"additional","affiliation":[]},{"given":"Heiko","family":"Vogler","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,10,28]]},"reference":[{"issue":"1","key":"9296_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0020-0190(87)90190-6","volume":"24","author":"A. Alexandrakis","year":"1987","unstructured":"Alexandrakis, A., Bozapalidis, S.: Weighted grammars and Kleene\u2019s theorem. Inf. Process. Lett. 24(1), 1\u20134 (1987)","journal-title":"Inf. Process. Lett."},{"key":"9296_CR2","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1007\/BF01893886","volume":"28","author":"S. Bozapalidis","year":"1991","unstructured":"Bozapalidis, S.: Effective construction of the syntactic algebra of a recognizable series on trees. Acta Inform. 28, 351\u2013363 (1991)","journal-title":"Acta Inform."},{"issue":"2","key":"9296_CR3","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0304-3975(82)90019-6","volume":"18","author":"J. Berstel","year":"1982","unstructured":"Berstel, J., Reutenauer, C.: Recognizable formal power series on trees. Theor. Comput. Sci. 18(2), 115\u2013148 (1982)","journal-title":"Theor. Comput. Sci."},{"key":"9296_CR4","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1002\/malq.19600060105","volume":"6","author":"J.R. B\u00fcchi","year":"1960","unstructured":"B\u00fcchi, J.R.: Weak second-order arithmetic and finite automata. Z.\u00a0Math. Log. Grundl. Math. 6, 66\u201392 (1960)","journal-title":"Z.\u00a0Math. Log. Grundl. Math."},{"key":"9296_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0304-3975(86)90050-2","volume":"42","author":"B. Courcelle","year":"1986","unstructured":"Courcelle, B.: Equivalences and transformations of regular systems\u2014applications to recursive program schemes and grammars. Theor. Comput. Sci. 42, 1\u2013122 (1986)","journal-title":"Theor. Comput. Sci."},{"key":"9296_CR6","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1016\/S0022-0000(70)80041-1","volume":"4","author":"J. Doner","year":"1970","unstructured":"Doner, J.: Tree acceptors and some of their applications. J.\u00a0Comput. Syst. Sci. 4, 406\u2013451 (1970)","journal-title":"J.\u00a0Comput. Syst. Sci."},{"key":"9296_CR7","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/11523468_42","volume-title":"Automata, Languages and Programming\u201432nd International Colloquium, ICALP 2005","author":"M. Droste","year":"2005","unstructured":"Droste, M., Gastin, P.: Weighted automata and weighted logics. In: Automata, Languages and Programming\u201432nd International Colloquium, ICALP 2005, Lisbon, Portugal. Lecture Notes in Comput. Sci., vol. 3580, pp. 513\u2013525. Springer, Berlin (2005)"},{"issue":"1\u20132","key":"9296_CR8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.tcs.2007.02.055","volume":"380","author":"M. Droste","year":"2007","unstructured":"Droste, M., Gastin, P.: Weighted automata and weighted logics. Theor. Comput. Sci. 380(1\u20132), 69\u201386 (2007)","journal-title":"Theor. Comput. Sci."},{"key":"9296_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-01492-5","volume-title":"Handbook of Weighted Automata","author":"M. Droste","year":"2009","unstructured":"Droste, M., Gastin, P.: Weighted automata and weighted logics. In: Droste, M., Kuich, W., Vogler, H. (eds.) Handbook of Weighted Automata. Springer, Berlin (2009), Chap.\u00a05"},{"key":"9296_CR10","series-title":"Lecture Notes in Comp. Sci.","first-page":"73","volume-title":"Proc. of Implementation and Application of Automata, 12th CIAA","author":"M. Droste","year":"2007","unstructured":"Droste, M., Rahonis, G.: Weighted automata and weighted logics with discounting. In: Holub, J., Zd\u00e1rek, J. (eds.) Proc. of Implementation and Application of Automata, 12th CIAA, Prague. Lecture Notes in Comp. Sci., vol. 4783, pp. 73\u201384. Springer, Berlin (2007)"},{"key":"9296_CR11","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.tcs.2006.08.025","volume":"366","author":"M. Droste","year":"2006","unstructured":"Droste, M., Vogler, H.: Weighted tree automata and weighted logics. Theor. Comput. Sci. 366, 228\u2013247 (2006)","journal-title":"Theor. Comput. Sci."},{"key":"9296_CR12","author":"M. Droste","year":"2009","unstructured":"Droste, M., Vogler, H.: Weighted logics for unranked tree automata. Theory Comput. Syst. (2009). doi: 10.1007\/s00224-009-9224-4","journal-title":"Theory Comput. Syst."},{"key":"9296_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1007\/978-3-642-14455-4_16","volume-title":"Proc. of 14th Int. Conf. on Developments in Language Theory, DLT","author":"M. Droste","year":"2010","unstructured":"Droste, M., Vogler, H.: Kleene and B\u00fcchi theorems for weighted automata and multi-valued logics over arbitrary bounded lattices. In: Proc. of 14th Int. Conf. on Developments in Language Theory, DLT. Lecture Notes in Computer Science, vol.\u00a06224, pp.\u00a0160\u2013172. Springer, Berlin (2010)"},{"key":"9296_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00224-004-1096-z","volume":"38","author":"M. Droste","year":"2005","unstructured":"Droste, M., Pech, C., Vogler, H.: A Kleene theorem for weighted tree automata. Theory Comput. Syst. 38, 1\u201338 (2005)","journal-title":"Theory Comput. Syst."},{"issue":"1","key":"9296_CR15","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0304-3975(95)00130-1","volume":"154","author":"W. Ebinger","year":"1996","unstructured":"Ebinger, W., Muscholl, A.: Logical definability on infinite traces. Theor. Comput. Sci. 154(1), 67\u201384 (1996)","journal-title":"Theor. Comput. Sci."},{"key":"9296_CR16","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1090\/S0002-9947-1961-0139530-9","volume":"98","author":"C.C. Elgot","year":"1961","unstructured":"Elgot, C.C.: Decision problems of finite automata design and related arithmetics. Trans. Am. Math. Soc. 98, 21\u201352 (1961)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"9296_CR17","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1007\/BF01704020","volume":"9","author":"J. Engelfriet","year":"1975","unstructured":"Engelfriet, J.: Bottom-up and top-down tree transformations\u2014a comparison. Math. Syst. Theory 9(3), 198\u2013231 (1975)","journal-title":"Math. Syst. Theory"},{"issue":"2","key":"9296_CR18","first-page":"219","volume":"8","author":"Z. \u00c9sik","year":"2003","unstructured":"\u00c9sik, Z., Kuich, W.: Formal tree series. J.\u00a0Autom. Lang. Comb. 8(2), 219\u2013285 (2003)","journal-title":"J.\u00a0Autom. Lang. Comb."},{"key":"9296_CR19","doi-asserted-by":"crossref","first-page":"1450","DOI":"10.1016\/j.fss.2007.02.016","volume":"158","author":"Z. \u00c9sik","year":"2007","unstructured":"\u00c9sik, Z., Liu, G.: Fuzzy tree automata. Fuzzy Sets Syst. 158, 1450\u20131460 (2007)","journal-title":"Fuzzy Sets Syst."},{"key":"9296_CR20","author":"I. Fichtner","year":"2009","unstructured":"Fichtner, I.: Weighted picture automata and weighted logics. Theory Comput. Syst. (2009). doi: 10.1007\/s00224-009-9225-3","journal-title":"Theory Comput. Syst."},{"key":"9296_CR21","volume-title":"Handbook of Weighted Automata","author":"Z. F\u00fcl\u00f6p","year":"2009","unstructured":"F\u00fcl\u00f6p, Z., Vogler, H.: Weighted tree automata and tree transducers. In: Droste, M., Kuich, W., Vogler,\u00a0H. (eds.) Handbook of Weighted Automata. Springer, Berlin (2009), Chap.\u00a09"},{"key":"9296_CR22","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s00224-007-9091-9","volume":"44","author":"Z. F\u00fcl\u00f6p","year":"2009","unstructured":"F\u00fcl\u00f6p, Z., Maletti, A., Vogler, H.: A\u00a0Kleene theorem for weighted tree automata over distributive multioperator monoids. Theory Comput. Syst. 44, 455\u2013499 (2009)","journal-title":"Theory Comput. Syst."},{"key":"9296_CR23","volume-title":"Tree Automata","author":"F. G\u00e9cseg","year":"1984","unstructured":"G\u00e9cseg, F., Steinby, M.: Tree Automata. Akad\u00e9miai Kiad\u00f3, Budapest (1984)"},{"key":"9296_CR24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-642-59126-6_1","volume-title":"Handbook of Formal Languages","author":"F. G\u00e9cseg","year":"1997","unstructured":"G\u00e9cseg, F., Steinby, M.: Tree languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol.\u00a03, pp. 1\u201368. Springer, Berlin (1997), Chap.\u00a01"},{"key":"9296_CR25","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1007\/978-3-642-59126-6_4","volume-title":"Handbook of Formal Languages, Part\u00a0III","author":"D. Giammarresi","year":"1997","unstructured":"Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, Part\u00a0III, pp. 215\u2013268. Springer, Berlin (1997)"},{"issue":"1","key":"9296_CR26","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1006\/inco.1996.0018","volume":"125","author":"D. Giammarresi","year":"1996","unstructured":"Giammarresi, D., Restivo, A., Seibert, S., Thomas, W.: Monadic second order logic over rectangular pictures and recognizability by tiling systems. Inf. Comput. 125(1), 32\u201345 (1996)","journal-title":"Inf. Comput."},{"key":"9296_CR27","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/B978-0-12-775260-0.50018-9","volume-title":"Fuzzy Sets and Their Applications to Cognitive and Decision Processes","author":"Y. Inagaki","year":"1975","unstructured":"Inagaki, Y., Fukumura, T.: On the description of fuzzy meaning of context-free languages. In: Fuzzy Sets and Their Applications to Cognitive and Decision Processes, pp. 301\u2013328. Academic Press, New York (1975)"},{"key":"9296_CR28","first-page":"61","volume-title":"Proceedings of the 3rd International Conference on Developments in Language Theory, DLT 1997","author":"W. Kuich","year":"1998","unstructured":"Kuich, W.: Formal power series over trees. In: Bozapalidis, S. (ed.) Proceedings of the 3rd International Conference on Developments in Language Theory, DLT 1997, Thessaloniki, Greece, pp. 61\u2013101. Aristotle University of Thessaloniki, Thessaloniki (1998)"},{"key":"9296_CR29","first-page":"1","volume-title":"Contributions to General Algebra 12\u2014Proceedings of the 58th Workshop on General Algebra \u201c58. Arbeitstagung Allgemeine Algebra\u201d","author":"W. Kuich","year":"1999","unstructured":"Kuich, W.: Linear systems of equations and automata on distributive multioperator monoids. In: Contributions to General Algebra 12\u2014Proceedings of the 58th Workshop on General Algebra \u201c58. Arbeitstagung Allgemeine Algebra\u201d, Vienna University of Technology, June 3\u20136, 1999, pp. 1\u201310. Johannes Heyn, Klagenfurt (1999)"},{"key":"9296_CR30","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/11523468_4","volume-title":"Automata, Languages and Programming: 32nd International Colloquium, ICALP 2005","author":"L. Libkin","year":"2005","unstructured":"Libkin, L.: Logics for unranked trees: an overview. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) Automata, Languages and Programming: 32nd International Colloquium, ICALP 2005, Lisbon, Portugal. Lecture Notes in Comput. Sci., vol. 3580, pp. 35\u201350. Springer, Berlin (2005)"},{"issue":"3:2","key":"9296_CR31","first-page":"1","volume":"2","author":"L. Libkin","year":"2006","unstructured":"Libkin, L.: Logics for unranked trees: an overview. Log. Methods Comput. Sci. 2(3:2), 1\u201331 (2006)","journal-title":"Log. Methods Comput. Sci."},{"key":"9296_CR32","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/978-3-540-30550-7_27","volume-title":"DLT\u201904\u20148th International Conference on Developments in Language Theory","author":"A. Maletti","year":"2004","unstructured":"Maletti, A.: Relating tree series transducers and weighted tree automata. In: Calude, C.S. (ed.) DLT\u201904\u20148th International Conference on Developments in Language Theory, Auckland, New Zealand, December 13\u201317, 2004. Lecture Notes in Comput. Sci., vol.\u00a0340, pp. 321\u2013333 (2004)"},{"issue":"4","key":"9296_CR33","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1142\/S012905410500325X","volume":"16","author":"A. Maletti","year":"2005","unstructured":"Maletti, A.: Relating tree series transducers and weighted tree automata. Int. J. Found. Comput. Sci. 16(4), 723\u2013741 (2005)","journal-title":"Int. J. Found. Comput. Sci."},{"key":"9296_CR34","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1007\/978-3-540-73208-2_31","volume-title":"Proc. of the 11th Int. Conf. on Developments in Language Theory, DLT","author":"C. Mathissen","year":"2007","unstructured":"Mathissen, C.: Definable transductions and weighted logics for texts. In: Proc. of the 11th Int. Conf. on Developments in Language Theory, DLT, Turku. Lecture Notes in Comput. Sci., vol. 4588, pp.\u00a0324\u2013336. Springer, Berlin (2007)"},{"key":"9296_CR35","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/978-3-540-70583-3_19","volume-title":"Proc. of the 35th Int. Colloquium on Automata, Languages and Programming, ICALP","author":"C. Mathissen","year":"2008","unstructured":"Mathissen, C.: Weighted logics for nested words and algebraic formal power series. In: Proc. of the 35th Int. Colloquium on Automata, Languages and Programming, ICALP, Reykjavik. Lecture Notes in Comput. Sci., vol. 5126, pp. 221\u2013232. Springer, Berlin (2008)"},{"key":"9296_CR36","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/11753728_25","volume-title":"Proc. of Computer Science\u2014Theory and Applications, 1st CSR","author":"I. Meinecke","year":"2006","unstructured":"Meinecke, I.: Weighted logics for traces. In: Proc. of Computer Science\u2014Theory and Applications, 1st CSR, St.\u00a0Petersburg. Lecture Notes in Comput. Sci., vol.\u00a03967, pp.\u00a0235\u2013246. Springer, Berlin (2006)"},{"key":"9296_CR37","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1007\/3-540-45793-3_2","volume-title":"Computer Science Logic: 16th International Workshop, CSL 2002","author":"F. Neven","year":"2002","unstructured":"Neven, F.: Automata, logic, and XML. In: Bradfield, J. (ed.) Computer Science Logic: 16th International Workshop, CSL 2002, Edinburgh, Scotland, UK. Lecture Notes in Comput. Sci., vol. 2471, pp.\u00a02\u201326. Springer, Berlin (2002)"},{"key":"9296_CR38","series-title":"Lecture Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/978-3-642-02737-6_34","volume-title":"Proc. of Developments in Language Theory 2009, 13th DLT","author":"K. Quaas","year":"2009","unstructured":"Quaas, K.: Weighted timed MSO logics. In: Proc. of Developments in Language Theory 2009, 13th DLT. Lecture Notes in Comput. Sci., vol. 5583, pp. 419\u2013430. Springer, Berlin (2009)"},{"key":"9296_CR39","unstructured":"Radovanovi\u0107, D.: Weighted tree automata over strong bimonoids. Novi Sad J.\u00a0Math. (2010, to appear)"},{"key":"9296_CR40","first-page":"455","volume":"12","author":"G. Rahonis","year":"2007","unstructured":"Rahonis, G.: Weighted Muller tree automata and weighted logics. J.\u00a0Autom. Lang. Program. 12, 455\u2013483 (2007)","journal-title":"J.\u00a0Autom. Lang. Program."},{"key":"9296_CR41","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1137\/0219027","volume":"19","author":"H. Seidl","year":"1990","unstructured":"Seidl, H.: Deciding equivalence of finite tree automata. SIAM J. Comput. 19, 424\u2013437 (1990)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"9296_CR42","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1142\/S012905410900653X","volume":"20","author":"T. St\u00fcber","year":"2009","unstructured":"St\u00fcber, T., Vogler, H., F\u00fcl\u00f6p, Z.: Decomposition of weighted multioperator tree automata. Int. J. Found. Comput. Sci. 20(2), 221\u2013245 (2009)","journal-title":"Int. J. Found. Comput. Sci."},{"issue":"1","key":"9296_CR43","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF01691346","volume":"2","author":"J.W. Thatcher","year":"1968","unstructured":"Thatcher, J.W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Syst. Theory 2(1), 57\u201381 (1968)","journal-title":"Math. Syst. Theory"}],"container-title":["Theory of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-010-9296-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00224-010-9296-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00224-010-9296-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T11:54:22Z","timestamp":1558698862000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00224-010-9296-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,28]]},"references-count":43,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["9296"],"URL":"https:\/\/doi.org\/10.1007\/s00224-010-9296-1","relation":{},"ISSN":["1432-4350","1433-0490"],"issn-type":[{"value":"1432-4350","type":"print"},{"value":"1433-0490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,28]]}}}